Browse Function problems Studdy Solved!

Problem 6001

Find $f^{\prime \prime}(x)$ $\begin{array}{r} f(x)=x^{1 / 9} \\ f^{\prime \prime}(x)=\square \end{array}$

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Problem 6002

The median weight of a boy whose age is between 0 and 36 months can be approximated by the function $w(t)=9.66+1.55 t-0.0076 t^{2}+0.000076 t^{3}$ where $t$ is measured in months and $w$ is measured in pounds. Use this approximation to find the following for a boy with median weight in parts a) through c) below. a) The rate of change of weight with respect to time. $w^{\prime}(t)=$ $\square$ b) The weight of the baby at age 11 months.
The approximate weight of the baby at age 11 months is $\square$ Ibs. (Round to two decimal places as needed.) c) The rate of change of the baby's weight with respect to time at age 11 months
The rate of change for the baby's weight with respect to time at age 11 months is approximately $\square$ lbs/month. (Round to two decimal places as needed.) Next

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Problem 6003

Suppose that $\$ 2100$ is initially invested in an account at a fixed interest rate, compounded continuously. Suppose also that, after two and a half years, the amount of money in the account is $\$ 2376$ . Find the interest rate per year.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth. $\square$ \% per year

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Problem 6004

Find the derivative of the function $f(t) = e^{2t} \ln(t+1)$ .

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Problem 6005

How much money is in an account after 10 years if $\$ 1900$ is invested at 4.1\% interest compounded: A) monthly? $\square$ B) weekly? $\square$ C) continuously? $\square$

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Problem 6006

Exercise 1. Determine limited development in the neighborhood of $x_{0}=0$ to the indicated order $n$ for the following functions
1. $\frac{1+x+x^{2}}{1+x+x^{3}} \quad(n=3){ }^{I}$
3. $\frac{\arctan (2 x)}{-1+\sin x} \quad(n=3)$ ,
2. $\sqrt{\frac{1+x}{2-x^{2}}} \quad(n=2)$
4. $\frac{\operatorname{sh}^{2} x}{\ln (\cos x)} \quad(n=2)$ ,
5. $e^{\sqrt{2+\cos x}} \quad(n=2)$
Exercise 2.
1. Determine the limited development in the neighborhood of $x_{0}$ to the indicated order $n$ of the following functions : (a) $f(x)=\cos x, x_{0}=\frac{\pi}{4}, n=3$ . (b) $\frac{\ln (x)}{x^{2}}\left(x_{0}=1, n=3\right)$ .
2. Determine Determine the limited development in the neighborhood of $+\infty$ to the indicated order $n$ of the following functions : (a) $f(x)=\frac{\sqrt{x+2}}{\sqrt{x}}, n=3$ (b) $\ln \left(x+\sqrt{1+x^{2}}\right)-\ln x(n=4)$

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Problem 6007

Exercise 1. Determine limited development in the neighborhood of $x_{0}=0$ to the indicated order $n$ for the following functions
1. $\frac{1+x+x^{2}}{1+x+x^{3}} \quad(n=3){ }^{I}$
3. $\frac{\arctan (2 x)}{-1+\sin x} \quad(n=3)$ ,
2. $\sqrt{\frac{1+x}{2-x^{2}}} \quad(n=2)$
4. $\frac{\operatorname{sh}^{2} x}{\ln (\cos x)} \quad(n=2)$ ,
5. $e^{\sqrt{2+\cos x}} \quad(n=2)$
Exercise 2.
1. Determine the limited development in the neighborhood of $x_{0}$ to the indicated order $n$ of the following functions : (a) $f(x)=\cos x, x_{0}=\frac{\pi}{4}, n=3$ . (b) $\frac{\ln (x)}{x^{2}}\left(x_{0}=1, n=3\right)$ .
2. Determine Determine the limited development in the neighborhood of $+\infty$ to the indicated order $n$ of the following functions : (a) $f(x)=\frac{\sqrt{x+2}}{\sqrt{x}}, n=3$ (b) $\ln \left(x+\sqrt{1+x^{2}}\right)-\ln x(n=4)$

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Problem 6008

The fox population in a certain region has an annual growth rate of 5 percent per year. (Note: Foxes mate once per year.)
It is estimated that the fox population in the year 2020 was 14000. (a) Find an exponential function that models the fox population $t$ years after 2020 (Note: $t=0$ for 2020). The function is $P(t)=$ $\square$ (b) Use the function from part (a) to estimate the fox population in the year 2028. (The answer should be an integer.) There will be $\square$ foxes in the year 2028.

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Problem 6009

Find functions $f$ and $g$ so that $f \circ g=H$ . $H(x)=(5 x+2)^{4}$
Choose the correct pair of functions. A. $f(x)=\sqrt[4]{x}, g(x)=\frac{x-2}{5}$ C. $f(x)=\frac{x-2}{5}, g(x)=\sqrt[4]{x}$ $B$ . $f(x)=x^{4}, g(x)=5 x+2$ D. $f(x)=5 x+2, g(x)=x^{4}$

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Problem 6010

Differentiate the following function. $\begin{array}{l} y=\frac{5 x^{4}}{(5-4 x)^{2}} \\ \frac{d y}{d x}=\square \end{array}$ $\square$

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Problem 6011

For $f(x)=\sqrt{x}$ and $g(x)=4 x+1$ , find the following composite functions and state the domain of each. (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $\mathrm{g} \circ \mathrm{g}$ (a) $(f \circ g)(x)=$ $\square$ (Simplify your answer.)
Select the correct choice below and fill in any answer boxes within your choice. A. The domain of $f \circ \mathrm{~g}$ is $\{\mathrm{x} \mid \square\}$ . $\square$ (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of $f \circ g$ is all real numbers. (b) $(g \circ f)(x)=$ $\square$ (Simplify your answer.)
Select the correct choice below and fill in any answer boxes within your choice. A. The domain of $g \circ f$ is $\{x$ $\square$ \}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of $g \circ f$ is all real numbers. (c) $(f \circ f)(x)=$ $\square$ (Simplify your answer.)
Select the correct choice below and fill in any answer boxes within your choice. A. The domain of $f$ o $f$ is $\{x$ $\square$ \}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of $f$ o $f$ is all real numbers.

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Problem 6012

Find an equation for the graph shown to the right.
Type the equation in the form $y=A \sin (\omega x)$ or $y=A \cos (\omega x)$ . $\mathrm{y}=\square$ (Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 6013

Find an equation for the graph shown to the right.
Type the equation in the form $y=A \sin (\omega x)$ or $y=A \cos (\omega x)$ . $y=\square$ (Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 6014

Find an equation for the graph shown to the right.
Type the equation in the form $y=A \sin (\omega x)$ or $y=A \cos (\omega x)$ . $y=\square$ (Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 6015

For the given function, find the indicated function values. Find the domain of the function. $f(x)=\sqrt{2 x+18}$ , find $f(0), f(1), f(4), f(-8)$ .

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Problem 6016

2 (Graded ASsignu
For the function on the right, determine whether the function is one-to-one.
Is the function one-to-one? No Yes

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Problem 6017

If $f(29)=26$ and $f$ is one-to-one, what is $f^{-1}(26) ?$ $f^{-1}(26)=$ $\square$

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Problem 6018

A fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides is to be made of material that costs : dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Dimensions: $\square$ x $\square$
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Problem 6019

Suppose that $\mathrm{G}(\mathrm{x})=\log _{3}(2 \mathrm{x}-1)-3$ . (a) What is the domain of G? (b) What is $\mathrm{G}(5)$ ? What point is on the graph of G ? (c) If $\mathrm{G}(\mathrm{x})=1$ , what is x ? What point is on the graph of G ? (d) What is the zero of $G$ ? (a) The domain of G is $\square$ . (Type your answer in interval notation.) (b) $G(5)=$ $\square$ The point $\square$ is on the graph of G. (Type an ordered pair.) (c) If $\mathrm{G}(\mathrm{x})=1$ , then $\mathrm{x}=$ $\square$ $\square$ .
The point $\square$ is on the graph of G. (Type an ordered pair.) (d) The zero of $G$ is $x=$ $\square$ $\square$ .

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Problem 6020

7. Find the value of $b$ that would cause the graph of $y=b^{x}$ to look like the graph below.

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Problem 6021

Find the domain of the function. $f(x)=\ln (x+3)$
The domain of f is $\square$ . (Type your answer in interval notation.)

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Problem 6022

The function $D(h)=8 e^{-0.51 \mathrm{~h}}$ can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. How many milligrams will be present after 1 hour? After 7 hours?
After 1 hour, there will be $\square$ milligrams. (Round to two decimal places as needed.) After 7 hours, there will be $\square$ milligrams. (Round to two decimal places as needed.)

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Problem 6023

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by $x=0, y=1, x=y^{15}$ about the line $y=10$ .

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Problem 6024

Decide which function is an antiderivative of the other: $f(x)=\frac{5}{\sqrt{x}} \quad g(x)=10 \sqrt{x}$
Choose one

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Problem 6025

Write the partial fraction decomposition $\frac{-2 x^{2}-3 x+13}{(x+2)\left(x^{2}-2 x+3\right)}$

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Problem 6026

NASA launches a rocket at $t=0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t)=-4.9 t^{2}+40 t+185$ .
Assuming that the rocket will splash down into the ocean, at that time does splashdown occur? The rocket splashes down after $\square$ seconds. (Round your answer to 2 decimals.)
How high above sea-level does the rocket get at its peak? The rocket peaks at $\square$ 266.63 0 meters above sea-level. (Round your answer to 2 decimals.) Question Help: $\square$ Video 1 $\square$ Video 2 $\square$ Message instructor Submit Question

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Problem 6027

The table below shows the amount of time each of the 15 students in an introductory biology class spent studying for the first exam, and the student's score on the exam out of 100. \begin{tabular}{|c|c|} \hline $x$ (minutes spent studying) & $y$ (score on exam in points) \\ \hline 150 & 98 \\ \hline 70 & 65 \\ \hline 100 & 74 \\ \hline 120 & 46 \\ \hline 60 & 72 \\ \hline 0 & 52 \\ \hline 10 & 35 \\ \hline 75 & 79 \\ \hline 120 & 80 \\ \hline 45 & 72 \\ \hline 50 & 80 \\ \hline 0 & 30 \\ \hline 10 & 56 \\ \hline 40 & 64 \\ \hline 30 & 81 \\ \hline \end{tabular}
To check this is entered correctly on your calculator, press [stat], go to CALC, and select "2:2-Var Stats". Run this on your two lists. When you scroll down the list, you should see $\Sigma x y=65155$
Enter the data into your calculator and obtain a linear equation of best fit using the linear regression feature. Type the equation here, in the form $y=m x+b$ . If necessary, round the values of $m$ and $b$ to three decimal places. $\square$ Based on your regression equation, what score would you predict for a student who has studied for 1 hour and 10 minutes? Round your answer to a whole number of points. $\square$ points Based on your regression equation, how much time should a "typical" student spend studying if they wanted to score at least 75 points on the exam? Round your answer up to the next full minute. $\square$ minutes

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Problem 6028

(2 points) Let $f(x)=7+\sqrt{x-9}$ . Then find each of the following, giving all domain (a) $f^{-1}(x)=$ $\square$ (b) The domain of $f$ is $\square$ (c) The domain of $f^{-1}$ is $\square$ (d) The range of $f$ is $\square$ (e) The range of $f^{-1}$ is $\square$

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Problem 6029

Graph the function and determine the $x$ -irtercept $y=-2 \log (x+5)-3$ $(0,4398)$ $(-5,0)$ $(-4.968,0)$ No x-intercept

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Problem 6030

Aab-5-wDemo-STA $\times \mid$ Dal Lab 16 - MATH-1018-A01 - Pre-C $\times \mid$ bat Assignment 11 - MATH-1018-A01 $\times \mid \square$ My Student Aid Assignment 11 | Knewton knewton.com/learn/course/9e2ba2d3-121d-42f9-bfd7-dd6829a2a6b3/assignment/6db1e2bb-00c9-41da-b33c-1012b9fe79c1 MATH-018-A01 - PRECCNLOULUS IN PRACTICE MSTERY $\leftarrow$ Assignment 11 URRENT OBJECTIVE SWITCH Use sinusoidal functions to solve real-world applications
Question The equation $T=0.6 \sin \left(\frac{\pi}{28}(t-1)\right)+101.0$ describes the body temperature of a pig in Fahrenheit, where $t$ is time in hours. What is the temperature of the pig to the nearest tenth of a degree when $t=3$ ? Do not include the units in your answer. NOTE: The angle is in radians.
Provide your answer below: \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline ( & & \multicolumn{5}{|c|}{ $\checkmark$ } & (1) \\ \hline 7 & 8 & 9 & $\div$ & $x$ & $y$ & $x^{2}$ & $\sqrt{ }$ \\ \hline 4 & 5 & 6 & × & $\frac{x}{\square}$ & $x \frac{\square}{\square}$ & $x \square$ & $x_{\square}$ \\ \hline 1 & 2 & 3 & - & < & $>$ & $\pm$ & \ \\ \hline 0 & - & , & + & \% & 。 & : & ( \square \\ \hline 4 & - & 6 & = & | | | & \pi$ & ） & \\ \hline \end{tabular} Search

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Problem 6031

Find the domain of the following rational function. $H(x)=\frac{-8 x^{2}}{(x-6)(x+2)}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of $H(x)$ is $(x \mid x \neq$ $\square$ 1. (Type an integer or a fraction, Use a comma to soparal B. The domain of $H(x)$ has no resitictions.

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Problem 6032

(2 points) Let $f(x)=3 x^{2}+3$ and $g(x)=2 x^{2}+8$ Find and simplify each of the following functions: (a) $(f+g)(x)=$ (b) $(f-g)(x)=$ (c) $(f \cdot g)(x)=$ (d) $\left(\frac{f}{g}\right)(x)=$ help (formulas)

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Problem 6033

Use the Intermediate Value Theorem to show that the polynomial $f(x)=x^{3}+x^{2}-4 x+46$ has a real zero between -5 and -2
Select the correct choice below and fill in the answer boxes to complete your choice.
$\square$ $\square$ A. Because $f(x)$ is a polynomial with $f(-5)=\square<0$ and $f(-2)=\square<0$ , the function has a real zero between -5 and -2 . B. Because $f(x)$ is a polynomial with $f(-5)=$ $\square$ $\square$ $>0$ and $\mathrm{f}(-2)=$ $<0$ , the function has a real zero between -5 and -2 . C. Because $f(x)$ is a polynomial with $f(-5)=$ $\square$ $<0$ and $f(-2)=$ $\square$ $>0$ , the function has a real zero between -5 and -2 . D. Because $f(x)$ is a polynomial with $f(-5)=$ $\square$ $>0$ and $\mathrm{f}(-2)=$ $\square$ $>0$ , the function has a real zero between -5 and -2 .

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Problem 6034

Question The equation $p=7000 \cos \left(\frac{\pi}{10} t\right)+45000$ describes the number of deer in a forest where $t$ is the number of years after 1972. What was the population in the year 1978 to the nearest whole number? NOTE: The angle is in radians.
Provide your answer below: $p=\square]^{\text {deer }}$

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Problem 6035

Previous Problem Problem List Next Problem (1 point) Express the function $y=4(x-7)^{5}$ as a composition $y=(f \circ g)(x)$ of two simpler functions. $f(x)=$ $\square$ $g(x)=$ $\square$ Help entering formulas After submitting an answer, you can get a hint and click "Show Me Another" to see a similar probler

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Problem 6036

(1 point) Given that $f(x)=|x|$ and $g(x)=7 x+2$ , calculate (a) $(f \circ g)(x)=$ $\square$ (b) $(g \circ f)(x)=$ $\square$ (c) $(g \circ g)(x)=$ $\square$

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Problem 6037

Determine the inverse of the following function: $f(x)=3^{x-1}+4$
Show your work using the Equation Editor tool.

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Problem 6038

Question The equation $d=5 \sin (24 t)$ measures the displacement of a swinging pendulum in simple harmonic motion. $t$ is measured in seconds and $d$ is measured in centimeters. What is the displacement, to the nearest centimeter, when $t=4$ ? NOTE: The angle is in radians.
Provide your answer below: $d=$ $\square$ Icm

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Problem 6039

A study is done on the number of bacteria cells in a petri dish. Suppose that the population size $P(t)$ after $t$ hours is given by the following exponential function. $P(t)=2500(0.82)^{t}$
Find the initial population size. $2500$
Does the function represent growth or decay? growth decay By what percent does the population size change each hour? $\square$ \% Explanation Check

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Problem 6040

Question Given that $\cot (x)=-\frac{5}{2}$ , what is $\cot (-x)$ ?
Provide your answer below:

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Problem 6041

Find the rational zeros and then the other zeros and factor into linear factors for the function $f(x) = 3x^{4} - 4x^{3} + x^{2} + 6x - 2$ .

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Problem 6042

This question: 1 point(s) possidle
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x -axis or touches the x -axis and turns around at each zero $f(x)=3(x-6)(x+1)^{3}$
Determine the zero(s). The zero(s) is/are $\square$ (Type integers or decimals. Use a comma to separate answers as needed.) Determine the multiplicities of the zero(s). Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. There are two zeros. The multiplicity of the largest zero is $\square$ . The multiplicity of the smallest zero is $\square$ . (Simplify your answers.) B. There are three zeros. The multiplicity of the largest zero is $\square$ . The multiplicity of the smallest zero is $\square$ . The multiplicity of the other zero is $\square$ . (Simplify your answers.) C. There is one zero. The multiplicity of the zero is $\square$ . (Simplify your answer.) Determine the behavior of the function at each zero. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The graph touches the $x$ -axis and turns around at all zeros. B. The graph crosses the $x$ -axis at all zeros. C. The graph crosses the $x$ -axis at $x=$ $\square$ and touches the $x$ -axis and turns around at $x=$ $\square$ I. (Simplify your answers. Type integers or decimals. Use a comma to separate answers as needed.)

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Problem 6043

Find $g(x)$ , where $g(x)$ is the translation 1 unit up of $f(x)=4|x+5|+8$ . Write your answer in the form $\mathrm{a}|\mathrm{x}-\mathrm{h}|+\mathrm{k}$ , where $\mathrm{a}, \mathrm{h}$ , and k are integers. $g(x)=$ Submit

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Problem 6044

Move the graph of the function $(x+0)^{\frac{1}{3}}$ to the left 5 units and provide the new equation.

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Problem 6045

$\text{Given the following data points:}$ \begin{align} &\text{Shoe size (pointure de Soulier): 6, Foot length (longueur du pied): 20, Height (hauteur): 146.5} \\ &\text{Shoe size (pointure de Soulier): 6.5, Foot length (longueur du pied): 24, Height (hauteur): 162} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): 22.5, Height (hauteur): 163} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): 23, Height (hauteur): 166} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): 18, Height (hauteur): 169} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): \text{unknown}, Height (hauteur): \text{unknown}} \end{align}
$\text{Using a linear model, predict the height for the last data point with a shoe size of 7.}$
$\text{Determine whether interpolation or extrapolation is used in this prediction.}$

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Problem 6046

Exercise 2: Streaming Services A movie streaming service provides one account per household, but multiple people in the same household can use the account to watch their favorite shows.
Question: Is the relation between households and streaming accounts a function? Why or why not?

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Problem 6047

Find $f+g, f-g, f g$ and $\frac{f}{g}$ . Determine the domain for each function. $f(x)=6 x-5, g(x)=x+6$ $(f+g)(x)=$ $\square$ (Simplify your answer.)

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Problem 6048

$\left(F(x)=\frac{\ln \left(4 x^{2}\right)}{x}\right)$

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Problem 6049

(1 point)
Evaluate the limit using L'Hospital's rule if necessary. $\lim _{x \rightarrow+\infty} \frac{x^{16}}{e^{x}}$
Answer: $\square$

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Problem 6050

(1 point)
Find two numbers differing by 34 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers are $\square$

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Problem 6051

5. DETAILS
MY NOTES OSCOLALG1 6.2.094.
Graph the transformation of $f(x)=6^{x}$ . $h(x)=6^{-x}$

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Problem 6052

Cled inly seiection
9 Multiple Choice 1 point
An airplane leaves the runway climbing at an angle of $\theta=\frac{\pi}{10}$ and with a speed of 275 feet per second. Find the altitude of the plane after 2 minutes. Round your answer to the nearest tenth. 10,197.6 feet 784.6 feet 15,692.4 feet 3386.1 feet
Clear my selection

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Problem 6053

ig integral. $\int x^{5} \sqrt{x^{3}+1} d x$

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Problem 6054

A bacteria culture initially contains 2500 bacteria and doubles every half hour.
Find the size of the bacterial population after 40 minutes. $\square$ Find the size of the bacterial population after 7 hours. $\square$

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Problem 6055

4. This graph shows the recommended maximum heart rate of a person, $R$ beats per minute, as a function of her or his age, a years, for a stress test. a. Why are there no intercepts on this graph? [1 mark total] b. What is the rate of change? What does it represent? [2 marks total] c. At what age is the recommended maximum heart rate 120 beats $/ \mathrm{min}$ ? [1 mark total] d. What is the approximate recommended maximum heart rate for a person aged 70? [1 mark total]

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Problem 6056

Select the correct sequence to convert days to seconds:
1. days $\rightarrow$ seconds
2. days $\rightarrow$ minutes $\rightarrow$ hours $\rightarrow$ seconds
3. days $\rightarrow$ hours $\rightarrow$ minutes $\rightarrow$ seconds
4. days $\rightarrow$ hours $\rightarrow$ seconds

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Problem 6057

Jordan flies 650 miles round-trip. How many trips must he make yearly to fly between 10400 and 28600 miles for Gold status? Express in interval notation.

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Problem 6058

Determine if each relation is a function and state the domain and range for each set of pairs.

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Problem 6059

Determine if each equation defines y as a function of $x$ : 11. $x+y=16$ , 12. $x+y=25$ , 13. $x^{2}+y=16$ , 14. $x^{2}+y=25$ , 15. $x^{2}+y^{2}=16$ , 16. $x^{2}+y^{2}=25$ , 17. $x=y^{2}$ , 18. $4 x=y^{2}$ .

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Problem 6060

How many total votes were cast if Rahm Emanuel received 218,217 votes, which is $45.63\%$ of the total?

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Problem 6061

Draw a line to model Chicago's population growth from 1880 (500,000) to 1930 (3,400,000) and find its equation.

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Problem 6062

Find $f(x)=\frac{x}{|x|}$ for: a. $f(6)$ , b. $f(-6)$ , c. $f\left(r^{2}\right)$ .

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Problem 6063

Graph the functions $f$ and $g$ for $x$ from -2 to 2, then describe how $g$ relates to $f$ . Examples:
39. $f(x)=x, g(x)=x+3$
40. $f(x)=x, g(x)=x-4$
41. $f(x)=-2x, g(x)=-2x-1$
42. $f(x)=-2x, g(x)=-2x+3$
43. $f(x)=x^{2}, g(x)=x^{2}+1$
44. $f(x)=x^{2}, g(x)=x^{2}-2$
45. $f(x)=|x|, g(x)=|x|-2$

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Problem 6064

Explain the relationship between the graphs of $g(x) = x^{2} + 1$ and $f(x) = x^{2}$ .

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Problem 6065

Calculate the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x)=-7x+6$ , where $h \neq 0$ .

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Problem 6066

Evaluate the function $f(x)=4 x^{2}+2 x-2$ at these points: (a) $f(0)$ , (b) $f(5)$ , (c) $f(-5)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(5 x)$ , (h) $f(x+h)$ .

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Problem 6067

Find the difference quotient for the function $f(x)=-4x+7$ : $\frac{f(x+h)-f(x)}{h}, h \neq 0$ . Simplify your answer.

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Problem 6068

Find the domain of the function $P(t)=\frac{\sqrt{t-5}}{2 t-14}$ . What is the domain?

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Problem 6069

设函数 $f(x)=e^{x}(x \neq 0)$ ，求 $f\left(x_{1}\right) \cdot f\left(x_{2}\right)$ 的结果。选项是：A. $f\left(x_{1}\right)+f\left(x_{2}\right)$ B. $f\left(x_{1}+x_{2}\right)$ C. $f\left(x_{1}\right)-f\left(x_{2}\right)$ D. $f\left(\frac{x_{1}}{x_{2}}\right)$

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Problem 6070

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find height $h(100)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

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Problem 6071

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ . Round to two decimal places.

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Problem 6072

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find height $h$ after 250 ft using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

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Problem 6073

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find the distance $x$ it travels using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

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Problem 6074

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

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Problem 6075

Find the derivatives of the following functions:
1. $f(x)=x^{4}-5 x^{3}+9 x^{2}-7 x+5$
2. $y=\frac{3 x^{2}-6 x}{x^{3}}$
3. $g(x)=8 \sqrt{x}-\frac{6}{\sqrt[3]{x^{2}}}$
4. $h(x)=\frac{3 x+2}{x^{2}+1}$
5. $f(x)=3 x(8 x-3)^{7}$
6. $f(x)=3 x^{4}-4 x^{2}+7 x-11$
7. $k(x)=x \sqrt{9-x^{2}}$
8. $f(x)=-3\left(2 x^{2}-5 x+1\right)$
9. $g(x)=\frac{x^{2}}{3}-\frac{3}{x^{2}}$
10. $y=\frac{9}{x^{2}}-\frac{8}{x^{3}}+\frac{2}{x^{4}}$
11. $y=\sqrt[3]{x^{2}-3 x+4}$
12. $y=5 x^{2}-5 \sqrt{x}-\frac{3}{x}$
13. $y=\sqrt{x}-\frac{1}{\sqrt{x}}$
14. $y=(3 x-2)(2 x+1)$
15. $y=\frac{\sqrt{x}+1}{\sqrt{x}-1}$
16. $f(x)=4 x^{3}-3 x^{2}+2 x$
17. $y=z^{5}-e^{z} \ln z$
18. $f(x)=2 e^{x}-8^{x}$

See Solution

Problem 6076

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Height is given by $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ . Find distance and max height.

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Problem 6077

Find the derivatives of these functions: 1. $f(x)=x^{4}-5 x^{3}+9 x^{2}-7 x+5$ ; 2. $g(x)=8 \sqrt{x}-\frac{6}{\sqrt[3]{x^{2}}}$ ; 3. $h(x)=\frac{3 x+2}{x^{2}+1}$ ; 4. $f(x)=3 x(8 x-3)^{7}$ ; 5. $f(x)=3 x^{4}-4 x^{2}+7 x-11$ ; 6. $k(x)=x \sqrt{9-x^{2}}$ ; 7. $f(x)=-3(2 x^{2}-5 x+1)$ ; 8. $g(x)=\frac{x^{2}}{3}-\frac{3}{x^{2}}$ ; 9. $y=\frac{9}{x^{2}}-\frac{8}{x^{3}}+\frac{2}{x^{4}}$ .

See Solution

Problem 6078

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find the distance to max height using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

See Solution

Problem 6079

Graph the functions $f(x)=\sqrt{x}$ and $g(x)$ for given $x$ values. Describe the relationship between $f$ and $g$ .

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Problem 6080

An airplane flies 3000 miles at 550 mph. Cost per passenger is $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$ . Find $C(550)$ .

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Problem 6081

An airplane flies 3000 miles at 550 mph. Cost per passenger is $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$ . Find cost with 50 mph headwind.

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Problem 6082

An airplane crosses 3000 miles at 550 mph. Find cost per passenger $C(x)$ with a 100 mph headwind. Round to nearest cent.

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Problem 6083

An airplane crosses the Atlantic Ocean (3000 miles) at 560 mph. Cost per passenger with a 100 mph tailwind is given by
$\theta(x)=150+\frac{x}{20}+\frac{32,000}{x}$
What is the cost per passenger? Round to the nearest cent.

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Problem 6084

Find the difference quotient of $f(x)=x^{2}+3$ : calculate $\frac{f(x+h)-f(x)}{h}$ for $h \neq 0$ and simplify.

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Problem 6085

Graph the functions $f(x)=\sqrt{x}$ and $g(x)$ for given $x$ values. Describe the relation between their graphs.

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Problem 6086

Find values of $p$ and $q$ for the false bi-conditional $p \leftrightarrow q$ . Options: True/False pairs.

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Problem 6087

Find the derivatives of the following functions:
10. $y=\frac{3 x^{2}-6 x}{x^{3}}$
11. $y=\sqrt[3]{x^{2}-3 x+4}$
12. $y=5 x^{2}-5 \sqrt{x}-\frac{3}{x}$
13. $y=\sqrt{x}-\frac{1}{\sqrt{x}}$
14. $y=(3 x-2)(2 x+1)$
15. $y=\frac{\sqrt{x}+1}{\sqrt{x}-1}$
16. $f(x)=4 x^{3}-3 x^{2}+2 x$
17. $y=z^{5}-e^{z} \ln z$
18. $f(x)=2 e^{x}-8^{x}$

See Solution

Problem 6088

Find fixed points of the sequence defined by $a_{n+1}=\frac{1}{2}\left(a_{n}+\frac{3}{a_{n}}\right)$ .

See Solution

Problem 6089

Find the rate of change of $y=\cos 5 x$ . Choices: A. $\sin 5 x$ , B. $5 \sin 5 x$ , C. $-\sin 5 x$ , D. $-5 \sin 5 x$ .

See Solution

Problem 6090

Find the value of $a_{8}=(-1)^{8}(3 \cdot 8+5)$ . What is the result? Options: -27, 27, 29, -29.

See Solution

Problem 6091

Find the $12^{\text{th}}$ term of the sequence $a_{n} = 3^{n} + 3n$ . Options: 1,296, 72, 1,764, 531,477.

See Solution

Problem 6092

Determine the domain of the function $f(x)=\log_{10}\left(\frac{x+2}{x-4}\right)$ .

See Solution

Problem 6093

A printing service has a set-up fee of \ $11.00 and charges \$0.15 per copy. Find the cost for 40 copies using$ C=11.00+0.15x$.

See Solution

Problem 6094

Raina's phone card has $C=45.00-0.06x$ . How much credit is left after 15 minutes of calls?

See Solution

Problem 6095

Combine the expression into one logarithm: $4 \log_{c} 9 + 5 \log_{c} 5$ .

See Solution

Problem 6096

Find the domains of the functions: a. $\frac{q(x)}{h(x)}$ , b. $q(h(x))$ , c. $h(q(x))$ where $q(x)=\frac{1}{\sqrt{x}}$ and $h(x)=x^{2}-25$ .

See Solution

Problem 6097

Find $f^{-1}(9)$ given that $\mathrm{f}(1)=9$ .

See Solution

Problem 6098

Find functions $f$ and $g$ such that $h(x)=(x+8)^{3}=f(g(x))$ . Use $f(x)=x^{3}$ or $g(x)=x+8$

See Solution

Problem 6099

Find the value of $h(-2)$ for the function $h(x)=4 x^{2}+5$ .

See Solution

Problem 6100

Find the value of $g(-2)$ given $f(x)=2 x+4$ , $g(x)=-4 x^{2}-4 x-2$ , and $h(x)=-2 x^{2}+4$ .

See Solution

Function

Problem 6001

Find f′′(x)f^{\prime \prime}(x)f′′(x) f(x)=x1/9f′′(x)=□\begin{array}{r} f(x)=x^{1 / 9} \\ f^{\prime \prime}(x)=\square \end{array}f(x)=x1/9f′′(x)=□​

Problem 6002

Problem 6003

Problem 6004

Find the derivative of the function f(t)=e2tln⁡(t+1) f(t) = e^{2t} \ln(t+1) f(t)=e2tln(t+1).

Problem 6005

How much money is in an account after 10 years if $1900\$ 1900$1900 is invested at 4.1\% interest compounded: A) monthly? □\square□ B) weekly? □\square□ C) continuously? □\square□

Problem 6006

Problem 6007

Problem 6008

Problem 6009

Problem 6010

Differentiate the following function. y=5x4(5−4x)2dydx=□\begin{array}{l} y=\frac{5 x^{4}}{(5-4 x)^{2}} \\ \frac{d y}{d x}=\square \end{array}y=(5−4x)25x4​dxdy​=□​ □\square□

Problem 6011

Problem 6012

Problem 6013

Problem 6014

Problem 6015

For the given function, find the indicated function values. Find the domain of the function. f(x)=2x+18f(x)=\sqrt{2 x+18}f(x)=2x+18​, find f(0),f(1),f(4),f(−8)f(0), f(1), f(4), f(-8)f(0),f(1),f(4),f(−8).

Problem 6016

2 (Graded ASsignuFor the function on the right, determine whether the function is one-to-one.Is the function one-to-one? No Yes

Problem 6017

If f(29)=26f(29)=26f(29)=26 and fff is one-to-one, what is f−1(26)?f^{-1}(26) ?f−1(26)? f−1(26)=f^{-1}(26)=f−1(26)= □\square□

Problem 6018

Problem 6019

Problem 6020

7. Find the value of bbb that would cause the graph of y=bxy=b^{x}y=bx to look like the graph below.

Problem 6021

Find the domain of the function. f(x)=ln⁡(x+3)f(x)=\ln (x+3)f(x)=ln(x+3)The domain of f is □\square□ . (Type your answer in interval notation.)

Problem 6022

Problem 6023

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by x=0,y=1,x=y15x=0, y=1, x=y^{15}x=0,y=1,x=y15 about the line y=10y=10y=10.

Problem 6024

Decide which function is an antiderivative of the other: f(x)=5xg(x)=10xf(x)=\frac{5}{\sqrt{x}} \quad g(x)=10 \sqrt{x}f(x)=x​5​g(x)=10x​Choose one

Problem 6025

Write the partial fraction decomposition −2x2−3x+13(x+2)(x2−2x+3)\frac{-2 x^{2}-3 x+13}{(x+2)\left(x^{2}-2 x+3\right)}(x+2)(x2−2x+3)−2x2−3x+13​

Problem 6026

Problem 6027

Problem 6028

Problem 6029

Graph the function and determine the xxx-irtercept y=−2log⁡(x+5)−3y=-2 \log (x+5)-3y=−2log(x+5)−3 (0,4398)(0,4398)(0,4398) (−5,0)(-5,0)(−5,0) (−4.968,0)(-4.968,0)(−4.968,0) No x-intercept

Problem 6030

Problem 6031

Problem 6032

Problem 6033

Problem 6034

Problem 6035

Problem 6036

(1 point) Given that f(x)=∣x∣f(x)=|x|f(x)=∣x∣ and g(x)=7x+2g(x)=7 x+2g(x)=7x+2, calculate (a) (f∘g)(x)=(f \circ g)(x)=(f∘g)(x)= □\square□ (b) (g∘f)(x)=(g \circ f)(x)=(g∘f)(x)= □\square□ (c) (g∘g)(x)=(g \circ g)(x)=(g∘g)(x)= □\square□

Problem 6037

Determine the inverse of the following function: f(x)=3x−1+4f(x)=3^{x-1}+4f(x)=3x−1+4Show your work using the Equation Editor tool.

Problem 6038

Problem 6039

Problem 6040

Question Given that cot⁡(x)=−52\cot (x)=-\frac{5}{2}cot(x)=−25​, what is cot⁡(−x)\cot (-x)cot(−x) ?Provide your answer below:

Problem 6041

Find the rational zeros and then the other zeros and factor into linear factors for the function f(x)=3x4−4x3+x2+6x−2 f(x) = 3x^{4} - 4x^{3} + x^{2} + 6x - 2 f(x)=3x4−4x3+x2+6x−2.

Problem 6042

Problem 6043

Problem 6044

Move the graph of the function (x+0)13(x+0)^{\frac{1}{3}}(x+0)31​ to the left 5 units and provide the new equation.

Problem 6045

Problem 6046

Exercise 2: Streaming Services A movie streaming service provides one account per household, but multiple people in the same household can use the account to watch their favorite shows.Question: Is the relation between households and streaming accounts a function? Why or why not?

Problem 6047

Find f+g,f−g,fgf+g, f-g, f gf+g,f−g,fg and fg\frac{f}{g}gf​. Determine the domain for each function. f(x)=6x−5,g(x)=x+6f(x)=6 x-5, g(x)=x+6f(x)=6x−5,g(x)=x+6 (f+g)(x)=(f+g)(x)=(f+g)(x)= □\square□ (Simplify your answer.)

Problem 6048

(F(x)=ln⁡(4x2)x)\left(F(x)=\frac{\ln \left(4 x^{2}\right)}{x}\right)(F(x)=xln(4x2)​)

Problem 6049

(1 point)Evaluate the limit using L'Hospital's rule if necessary. lim⁡x→+∞x16ex\lim _{x \rightarrow+\infty} \frac{x^{16}}{e^{x}}x→+∞lim​exx16​Answer: □\square□

Problem 6050

(1 point)Find two numbers differing by 34 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers are □\square□

Problem 6051

5. DETAILSMY NOTES OSCOLALG1 6.2.094.Graph the transformation of f(x)=6xf(x)=6^{x}f(x)=6x. h(x)=6−xh(x)=6^{-x}h(x)=6−x

Problem 6052

Problem 6053

ig integral. ∫x5x3+1dx\int x^{5} \sqrt{x^{3}+1} d x∫x5x3+1​dx

Problem 6054

Find $f^{\prime \prime}(x)$ $\begin{array}{r} f(x)=x^{1 / 9} \\ f^{\prime \prime}(x)=\square \end{array}$

Find the derivative of the function $f(t) = e^{2t} \ln(t+1)$ .

How much money is in an account after 10 years if $\$ 1900$ is invested at 4.1\% interest compounded: A) monthly? $\square$ B) weekly? $\square$ C) continuously? $\square$

Differentiate the following function. $\begin{array}{l} y=\frac{5 x^{4}}{(5-4 x)^{2}} \\ \frac{d y}{d x}=\square \end{array}$ $\square$

For the given function, find the indicated function values. Find the domain of the function. $f(x)=\sqrt{2 x+18}$ , find $f(0), f(1), f(4), f(-8)$ .

2 (Graded ASsignu
For the function on the right, determine whether the function is one-to-one.
Is the function one-to-one? No Yes

If $f(29)=26$ and $f$ is one-to-one, what is $f^{-1}(26) ?$ $f^{-1}(26)=$ $\square$

7. Find the value of $b$ that would cause the graph of $y=b^{x}$ to look like the graph below.

Find the domain of the function. $f(x)=\ln (x+3)$
The domain of f is $\square$ . (Type your answer in interval notation.)

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by $x=0, y=1, x=y^{15}$ about the line $y=10$ .

Decide which function is an antiderivative of the other: $f(x)=\frac{5}{\sqrt{x}} \quad g(x)=10 \sqrt{x}$
Choose one

Write the partial fraction decomposition $\frac{-2 x^{2}-3 x+13}{(x+2)\left(x^{2}-2 x+3\right)}$

Graph the function and determine the $x$ -irtercept $y=-2 \log (x+5)-3$ $(0,4398)$ $(-5,0)$ $(-4.968,0)$ No x-intercept

(1 point) Given that $f(x)=|x|$ and $g(x)=7 x+2$ , calculate (a) $(f \circ g)(x)=$ $\square$ (b) $(g \circ f)(x)=$ $\square$ (c) $(g \circ g)(x)=$ $\square$

Determine the inverse of the following function: $f(x)=3^{x-1}+4$
Show your work using the Equation Editor tool.

Question Given that $\cot (x)=-\frac{5}{2}$ , what is $\cot (-x)$ ?
Provide your answer below:

Find the rational zeros and then the other zeros and factor into linear factors for the function $f(x) = 3x^{4} - 4x^{3} + x^{2} + 6x - 2$ .

Move the graph of the function $(x+0)^{\frac{1}{3}}$ to the left 5 units and provide the new equation.

Exercise 2: Streaming Services A movie streaming service provides one account per household, but multiple people in the same household can use the account to watch their favorite shows.
Question: Is the relation between households and streaming accounts a function? Why or why not?

Find $f+g, f-g, f g$ and $\frac{f}{g}$ . Determine the domain for each function. $f(x)=6 x-5, g(x)=x+6$ $(f+g)(x)=$ $\square$ (Simplify your answer.)

$\left(F(x)=\frac{\ln \left(4 x^{2}\right)}{x}\right)$

(1 point)
Evaluate the limit using L'Hospital's rule if necessary. $\lim _{x \rightarrow+\infty} \frac{x^{16}}{e^{x}}$
Answer: $\square$

(1 point)
Find two numbers differing by 34 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers are $\square$

5. DETAILS
MY NOTES OSCOLALG1 6.2.094.
Graph the transformation of $f(x)=6^{x}$ . $h(x)=6^{-x}$

ig integral. $\int x^{5} \sqrt{x^{3}+1} d x$

A bacteria culture initially contains 2500 bacteria and doubles every half hour.
Find the size of the bacterial population after 40 minutes. $\square$ Find the size of the bacterial population after 7 hours. $\square$

Determine if each equation defines y as a function of $x$ : 11. $x+y=16$ , 12. $x+y=25$ , 13. $x^{2}+y=16$ , 14. $x^{2}+y=25$ , 15. $x^{2}+y^{2}=16$ , 16. $x^{2}+y^{2}=25$ , 17. $x=y^{2}$ , 18. $4 x=y^{2}$ .

How many total votes were cast if Rahm Emanuel received 218,217 votes, which is $45.63\%$ of the total?

Find $f(x)=\frac{x}{|x|}$ for: a. $f(6)$ , b. $f(-6)$ , c. $f\left(r^{2}\right)$ .

Explain the relationship between the graphs of $g(x) = x^{2} + 1$ and $f(x) = x^{2}$ .

Calculate the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x)=-7x+6$ , where $h \neq 0$ .

Evaluate the function $f(x)=4 x^{2}+2 x-2$ at these points: (a) $f(0)$ , (b) $f(5)$ , (c) $f(-5)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(5 x)$ , (h) $f(x+h)$ .

Find the difference quotient for the function $f(x)=-4x+7$ : $\frac{f(x+h)-f(x)}{h}, h \neq 0$ . Simplify your answer.

Find the domain of the function $P(t)=\frac{\sqrt{t-5}}{2 t-14}$ . What is the domain?

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find height $h(100)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ . Round to two decimal places.

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find height $h$ after 250 ft using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find the distance $x$ it travels using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .

A golf ball is hit at 130 ft/s at $45^{\circ}$ . Find $h(400)$ using $h(x)=\frac{-32 x^{2}}{130^{2}}+x$ .