Function

Problem 101

r(x)=2xs(x)=x\begin{array}{l} r(x)=2 \sqrt{x} \\ s(x)=\sqrt{x} \end{array} (rs)(3)=\left(\frac{r}{s}\right)(3)=

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Problem 102

Fri Sep 6 student.ex.edgenuity.com Algebra II Function Operations 54:27 If f (x) = 4-² and g(x) = 6x, which expression is equivalent to (g- f) (3)? 6-3-(4+3) 6-3-(4-32) 6(3)-4+32 6(3)-4-32 F 40% uiz Mark And Return 7 of 10 Save & Exit

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Problem 103

EXERCISES
1. Draw the graphs of the functions with the function values as given : (i) f(x)={1, when x01, when x>0f(x)=\left\{\begin{array}{rr}1, & \text { when } x \leq 0 \\ -1, & \text { when } x>0\end{array}\right. (ii) f(x)={x, when 0x<121x, when 12x1f(x)=\left\{\begin{aligned} x, & \text { when } 0 \leq x<\frac{1}{2} \\ 1-x, & \text { when } \frac{1}{2} \leq x \leq 1\end{aligned}\right. (iii) f(x)={x, when 0x122x, when 12<x<1f(x)=\left\{\begin{aligned} x, & \text { when } 0 \leq x \leq \frac{1}{2} \\ 2-x, & \text { when } \frac{1}{2}<x<1\end{aligned}\right. (iv) f(x)={x, when 0x<121, when x=121x, when 12<x<1f(x)=\left\{\begin{aligned} x, & \text { when } 0 \leq x<\frac{1}{2} \\ 1, & \text { when } x=\frac{1}{2} \\ 1-x, & \text { when } \frac{1}{2}<x<1\end{aligned}\right. (v) f(x)={x2, when x0x, when x>0f(x)=\left\{\begin{array}{ll}x^{2}, & \text { when } x \leq 0 \\ \sqrt{x}, & \text { when } x>0\end{array}\right. (vi) f(x)={1/x, when x<00, when x=01/x, when x>0f(x)=\left\{\begin{array}{rr}1 / x, & \text { when } x<0 \\ 0, & \text { when } x=0 \\ -1 / x, & \text { when } x>0\end{array}\right.

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Problem 104

Se define I(q)=7q211q+3\boldsymbol{I}(q)=7 q^{2}-11 q+3 como el ingreso de un producto y C(q)=7q+8\boldsymbol{C}(\boldsymbol{q})=7 q+8 como el costo de producirlo. a. Determine la utilidad del producto U(q)U(q) b. Calcule C(3)I(3)U(8)I(30)U(20)C(10)\cdot C(3) \cdot I(3) \cdot U(8) \cdot I(30) \cdot U(20) \cdot C(10) c. Determine los valores de q tales que U(q)=40U(q)=40 d. En que momento el ingreso es cero

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Problem 105

Luke is driving home from work. Let D(t)D(t) stand for Luke's remaining distance to drive DD (measured in Miles) after tt minutes of driving. What does D(0)=10D(0)=10 mean?

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Problem 106

5. Answer the following questions; a) Find the slope of the curve f(x)=x1f(x)=\sqrt{x-1} at the point x=5x=5.
Ans: \qquad

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Problem 107

Find the average rate of change of the function over the given interval. R(θ)=5θ+1R(\theta)=\sqrt{5 \theta+1} ΔRΔθ=\frac{\Delta R}{\Delta \theta}= \square (Simplify your answer.)

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Problem 108

Find the domain of the function. f(x)=x29f(x)=x^{2}-9

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Problem 109

The profits of a small company for each of the first five years of its operation are given in the table to the right. a. Plot points representing the profit as a function of year, and join them by as smooth a curve as you can. b. What is the average rate of increase of the profits between 2012 and 2014? \begin{tabular}{cc} \hline Year & Profit in $10005\boldsymbol{\$ 1 0 0 0 5} \\ \hline 2010 & 139 \\ 2011 & 160 \\ 2012 & 195 \\ 2013 & 244 \\ 2014 & 307 \\ \hline \end{tabular} c. Use your graph to estimate the rate at which the profits were changing in 2013. A. B. c. D. b. The average rate of increase of the profits between 2012 and 2014 is $56,000\$ 56,000 per year. (Round to the nearest thousand as needed.) c. The rate at which the profits were changing in 2013 is $\$ \square per year. (Round to the nearest thousand as needed.)

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Problem 110

If f(x)=x+1f(x)=x+1 and g(x)=x1g(x)=x-1, (a) f(g(x))=f(g(x))= \square (b) g(f(x))=g(f(x))= \square (c) Thus g(x)g(x) is called an \square function of f(x)f(x) Question Help: Video

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Problem 111

Suppose f(x)=8xf(x)=8^{x}. a) What is the domain of f1(x)f^{-1}(x) ? Enter your answer using interval notation. 1 [] U \infty π\pi aa^{\circ} aba^{b} a\sqrt{a} \square sin\sin \square Previev Invalid Inpu b) What is the range of f1(x)f^{-1}(x) ? Enter your answer using interval notation.

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Problem 112

y=x4+12xdydx=?y=x^{4}+12 x \quad \frac{d y}{d x}=?

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Problem 113

61 N. From the tables of values that appear next, mark with x\boldsymbol{x} those that repre- \begin{tabular}{|c|c|} \hline of proportional \\ \hlineTT & dd \\ \hline 0 & 0 \\ \hline 1 & 3 \\ \hline 2 & 6 \\ \hline 3 & 9 \\ \hline 4 & 12 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hlineFF & PP \\ \hline 10 & 101 \\ \hline 20 & 201 \\ \hline 30 & 301 \\ \hline 40 & 401 \\ \hline 50 & 501 \\ \hline \end{tabular} v. Graph the linear function f(x)=5x6f(x)=5 x-6, from its slope and its intercept. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline & & & & & & \mid & \mid & \mid \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline \end{tabular}
Given the function f(x)=2x+x2f(x)=2 x+x^{2}, draw its graph to indicate the intersections with the axes, the coordinate of the vertex and the maximum or minimum value of the ordinate.
Intersection with the xx-axis: \qquad Intersection with the yy-axis: \qquad
Intersection with the yy-axis: \qquad
Minimum or maximum value of the ordinate: \qquad
Equation of the axis of symmetry: \qquad

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Problem 114

The graphs of ff and gg are shown. Evaluate the function at the given values of xx, if possible. Write your answers as integers or simplified fractions. Select "Undefined" if applicable.
Part 1 of 7 (f+g)(4)(f+g)(4) is \square . Undefined

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Problem 115

In problems 6 and 7: {f(x)=(x3)2g(x)=4x2+2x82h(x)=18x+14\left\{\begin{array}{c} f(x)=(x-3)^{2} \\ g(x)=4 x^{2}+2 x-82 \\ h(x)=18 x+14 \end{array}\right.
Find h(h(1/2k/3))h(h(1 / 2-k / 3))

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Problem 116

and Graphs in of each of the following functions as an interval (or union of intervals) and intercepts for ff and gg f(x)=xx216D1(,4)(4,)g(x)=7x51,h(x)=3xx2+7x+103]10,3\begin{array}{c} f(x)=\frac{x}{x^{2}-16} D_{1}^{\prime}(-\infty, 4) \cup(4, \infty) \\ g(x)=\sqrt{\frac{7}{x-5}} \int_{1}^{\prime}, \infty \\ \left.h(x)=\frac{\sqrt{3-x}}{\sqrt[3]{x^{2}+7 x+10}}\right]_{1}^{0}-\infty, 3 \end{array}

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Problem 117

For the following function, make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at the indicated point. f(x)=14cosx at x=π2f(x)=14 \cos x \text { at } x=\frac{\pi}{2}
Complete the table below. (Round the final answer to three decimal places as needed. Round all intermediate values to four decimal places as needed.) \begin{tabular}{|c|c|} \hline Interval & Slope of secant line \\ \hline[π2,π]\left[\frac{\pi}{2}, \pi\right] & \square \\ \hline \end{tabular}

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Problem 118

After alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours. Suppose you have had three alcoholic drinks and an hour later, at midnight, your blood alcohol concentration (BAC) is 0.3mg/mL0.3 \mathrm{mg} / \mathrm{mL}. (a) Find an exponential decay model for your BAC tt hours after midnight. C(t)=C(t)= \square (b) Graph your BAC and use the graph to determine when you can drive home if the legal limit is 0.08mg/mL0.08 \mathrm{mg} / \mathrm{mL}. (Round your answer to one decimal place.) \qquad hr

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Problem 119

First find f+g,fg,fgf+g, f-g, f g, and fg\frac{f}{g}. Then determine the domain for each function. f(x)=x+8;g(x)=x1f(x)=\sqrt{x+8} ; g(x)=\sqrt{x-1}

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Problem 120

The function f(x)=2x321x2+36x+2f(x)=2 x^{3}-21 x^{2}+36 x+2 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema.
This function has a local minimum at x=x= \square with output value \square and a local maximum at x=x= \square with output value \square \qquad Hint: Adjust the Interval (Points A and B) to focus the attention around where you think the local max and local min will be. \qquad

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Problem 121

For f(x)=x+1f(x)=x+1 and g(x)=5x+3g(x)=5 x+3, find the following functions. a. (fg)(x);b.(gf)(x);(f \circ g)(x) ; b .(g \circ f)(x) ; c. (fg)(1);d.(gf)(1)(f \circ g)(1) ; d .(g \circ f)(1) a. (fg)(x)=(f \circ g)(x)= \square (Simplify your answer.)

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Problem 122

5. State whether each is a disk/washer or shell is needed to find the volume of the solid of revolution. Write the integral needed (there is no evaluation to do). a. A function bounded by f(x)f(x) and g(x)g(x) on an interval [1,5][1,5] revolved around the xx-axis b. A function bounded by f(x)f(x) and g(x)g(x) on an interval [1,5][1,5] revolved around the x=6x=6 c. A function of yy in the first quadrant bounded by g(y),y=0g(y), y=0, and x=0x=0, revolved around x=3x=-3. d. A function of yy in the first quadrant bounded by g(y),y=0g(y), y=0, and x=0x=0, revolved around y=2y=-2.

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Problem 123

For f(x)=2x4f(x)=2 x-4 and g(x)=2x21g(x)=2 x^{2}-1, find the following functions. a. (fg)(x);b(gf)(x);c(fg)(1);d.(gf)(1)(f \circ g)(x) ; b \cdot(g \circ f)(x) ; c \cdot(f \circ g)(-1) ; d .(g \circ f)(-1) a. (fg)(x)=(f \circ g)(x)= \square (Simplify your answer.)

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Problem 124

Express the given function hh as a composition of two functions ff and gg so that h(x)=(fg)(x)h(x)=(f \circ g)(x), where one of the functions is x36x^{3}-6. h(x)=x364h(x)=\sqrt[4]{x^{3}-6} f(x)=f(x)= \square (Simplify your answer.)

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Problem 125

Let f(x)=3x2+7f(x)=3 x^{2}+7 and g(x)=49xg(x)=4-9 x. Find (fg)(x)=f(x)g(x)(f g)(x)=f(x) g(x). (fg)(x)=27x363x(f g)(x)=-27 x^{3}-63 x (fg)(x)=27x363x+28(f g)(x)=-27 x^{3}-63 x+28 (fg)(x)=27x3+12x263x+28(f g)(x)=-27 x^{3}+12 x^{2}-63 x+28 (fg)(x)=3x29x+28(f g)(x)=3 x^{2}-9 x+28

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Problem 126

Find an equation for the tangent line to the graph of the given function at (2,7)(-2,7) f(x)=x2+3f(x)=x^{2}+3
Find an equation for the tangent line to the graph of f(x)=x2+3f(x)=x^{2}+3 at (2,7)(-2,7). y=y=

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Problem 127

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership of $90\$ 90 and you pay 40%40 \% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $40\$ 40 and you pay 60%60 \% of the mánufacturer's list price. a. Express the total yearly amount paid to the warehouse under plan A,fA, f, as a function of the dollars of merchandise purchased during the year, xx. f(x)=90+0.40xf(x)=90+0.40 x (Use integers or decimals for any numbers in the expression.) b. Express the total yearly amount paid to the warehouse under plan B, gg, as a function of the dollars of merchandise purchased during the year, xx. g(x)=g(x)= \square (Use integers or decimals for any numbers in the expression.)

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Problem 128

Fill in the blank. Let θ\theta be an angle in standard position with (x,y)(x, y) a point on the terminal side of θ\theta and r=x2+y20r=\sqrt{x^{2}+y^{2}} \neq 0. sin(θ)=\sin (\theta)= \square

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Problem 129

a. Use the product rule to find the derivative of the given function. b. Find the derivative by expanding the product first. h(z)=(4z2)(z32z+5)h(z)=\left(4-z^{2}\right)\left(z^{3}-2 z+5\right) a. Use the product rule to find the derivative of the given function. Select the correct answer below and fill in the answer box(es) to complete your choice. A. The derivative is (4z2)(z32z+5)\left(4-z^{2}\right)\left(z^{3}-2 z+5\right) \square ). B. The derivative is (z32z+5)\left(z^{3}-2 z+5\right) \square ). C. The derivative is (4z2)()\left(4-z^{2}\right)(\square). D. The derivative is (4z2)()+(z32z+5)()\left(4-z^{2}\right)(\square)+\left(z^{3}-2 z+5\right)(\square). E. The derivative is (4z2)(z32z+5)+()\left(4-z^{2}\right)\left(z^{3}-2 z+5\right)+(\square).

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Problem 130

a) Use the Quotient Rule to find the derivative of the given function. b) Find the derivative by dividing the expressions first. y=x6x4 for x0y=\frac{x^{6}}{x^{4}} \text { for } x \neq 0 a) Use the Quotient Rule to find the derivative of the given function. Select the correct answer below and fill in the answer box(es) to complete your choice. A. The derivative is x6()+x4()x8\frac{x^{6} \cdot(\square)+x^{4}(\square)}{x^{8}} B. The derivative is x6()x4()x6\frac{x^{6} \cdot(\square)-x^{4}(\square)}{x^{6}}. C. The derivative is x4()x6()x8\frac{x^{4} \cdot(\square)-x^{6}(\square)}{x^{8}}. D. The derivative is x4()x6()x6\frac{x^{4} \cdot(\square)-x^{6}(\square)}{x^{6}}

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Problem 131

The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t)=5cos(9t)y(t)=5 \cos (9 t), where yy is the displacement in centimeters and tt is the time in seconds. Find the displacement when t=0,t=14t=0, t=\frac{1}{4}, and t=i2t=\frac{i}{2}. (Round your answers to two decimal places.) (a) t=0t=0 \qquad cm (b) t=14t=\frac{1}{4}

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Problem 132

Differentiate the function. y=x2+10dydx=\begin{array}{l} y=\sqrt{x^{2}+10} \\ \frac{d y}{d x}=\square \end{array}

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Problem 133

Differentiate the function. y=(2x26)10dydx=\begin{array}{l} y=\left(2 x^{2}-6\right)^{-10} \\ \frac{d y}{d x}=\square \end{array} \square

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Problem 134

Differentiate the function. y=(3x2)5(5x5)2dydx=\begin{array}{l} y=(3 x-2)^{5}\left(5-x^{5}\right)^{2} \\ \frac{d y}{d x}=\square \end{array} \square

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Problem 135

Find the arc length of the graph of the function f(x)=3x3f(x)=3 \sqrt{x^{3}} from x=4x=4 to x=8x=8. Round your answer to 3 decimal places. You may use Desmos to compute the relevant definite integral. arc length ==
Submit answer Next item

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Problem 136

Current Attempt in Progress Are the two functions r(x)=2(x4)+10r(x)=2(x-4)+10 and s(x)=2x2s(x)=2 x-2 the same function?

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Problem 137

Use Desmos to compute the arc length of the graph of y=xsin(x)y=x \sin (x) from x=0x=0 to x=πx=\pi, rounded to 4 decimal places.
The arc length is \square

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Problem 138

aluate the following limit. Give an exact answer if the limit is a number. Otherwise, enter -\infty or \infty if the it is infinite, or enter DNE if the limit does not exist in another way. limb21b12b2=\lim _{b \rightarrow 2} \frac{\frac{1}{b}-\frac{1}{2}}{b-2}= \square bmit answer Next item

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Problem 139

Evaluate the following limit. Give an exact answer if the limit is a number. Otherwise, enter -\infty or \infty if the limit is infinite, or enter DNE if the limit does not exist in another way. limx8x+175x8=\lim _{x \rightarrow 8} \frac{\sqrt{x+17}-5}{x-8}= \square
Submit answer Next item

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Problem 140

Attempt 3: The answer is incorrect.
Select the Get help button to view a step-by-step solution guide.
Find the arc length of the graph of the function f(x)=3x3f(x)=3 \sqrt{x^{3}} from x=4x=4 to x=8x=8 Round your answer to 3 decimal places. You may use Desmos to compute the relevant definite integral. arc length =99.429=99.429
Try again Next item

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Problem 141

nd the following for the given functions. f(x)=x2+3,g(x)=6xf(x)=x^{2}+3, \quad g(x)=\sqrt{6-x} (a) (f+g)(x)=(f+g)(x)= \square (b) (fg)(x)=(f-g)(x)= \square (c) (fg)(x)=(f g)(x)= \square (d) (f/g)(x)=(f / g)(x)= \square
What is the domain of f/gf / g ? (Enter your answ

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Problem 142

The point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle. (312,215)sinθ=cosθ=tanθ=cscθ=secθ=cotθ=\begin{array}{l} \left(3 \frac{1}{2},-2 \sqrt{15}\right) \\ \sin \theta=\square \\ \cos \theta=\square \\ \tan \theta=\square \\ \csc \theta=\square \\ \sec \theta=\square \\ \cot \theta=\square \end{array}

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Problem 143

Question Watch Video Show Examples Given that f(x)=x2+7x18f(x)=x^{2}+7 x-18 and g(x)=x+9g(x)=x+9, find (f÷g)(x)(f \div g)(x) and express the result as a polynomial in simplest form.

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Problem 144

1. Qual ê a definicào de funçào de produçio? a) 1 relaçato entre o custo total e a quantidade produzida. b) A relagalo contre os inputs utilizados c a quantidade de output produrido c) A relaçalo entre o preço do produto e o preço dos fatores de prodles,atin
2. Uma isoquanta representa: a) Todos os niveis de produção que podem ser obtidos com diferentes combinitstieo die dois inpuls, mantendo constante o nivel de produçäo. b) A relagto entre custo total e quantidade produzida. c) As combinaccies de inputs que minimizam o custo de produgão.
3. O que representa a inclinação da curva de isocusto? a) A taxa a yue o capital pode ser substituido pelo trabatho, manitendo o wisto letish constante. bit relackio eccre o custo marginal e a receita marginal. c) A quantidade de capital necessária para aumentar a produçäo erm uma urhilades.
4. Se prece do capital aumeatar e 0 preco do trabatho se mantiver consfante, 9 guo acvateceri cum a reta de isocusto? a) A ibclinacäo da isocusto ficari mais inclinarla, favorecendo o trabalino. b. A inclinacio da isocusto naio serí afetada C) Arem de iscusom irt desloctr-se paralelamente para a diritita. S. A recesita marginal de uma cmpresa é definida comos 6) Oi cresto adicional de guodurir uma umidade enta de produtios

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Problem 145

Function gg can be thought of as a translated (shifted) version of f(x)=x2f(x)=x^{2}.
Write the equation for g(x)g(x). g(x)=g(x)= \square

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Problem 146

At a parking garage in a large city, the charge for parking consists of a flat fee of $1.00\$ 1.00 plus $1.50/hr\$ 1.50 / \mathrm{hr}. (a) Write a linear function to model the cost for parking P(t)P(t) for tt hours. (b) Evaluate P(1.7)P(1.7) and interpret the meaning in the context of this problem.

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Problem 147

This is Section 2.3 Problem 8:8:
For the function f(x)=5xf(x)=\frac{5}{x} (a) A simplified form of the difference quotient f(x+h)f(x)h\frac{f(x+h)-f(x)}{h}, when h0h \neq 0, is \square (b) Use the simplified form to compute the difference quotient for the following. Keep 3 decimal places (rounded). When x=2x=2 and h=0.5h=0.5, the difference quotient is \square When x=2x=2 and h=0.1h=0.1, the difference quotient is \square When x=2x=2 and h=0.01h=0.01, the difference quotient is \square When x=2x=2 and h=0.001h=0.001, the difference quotient is \square

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Problem 148

This is Section 2.3 Problem 12 :
For the function f(x)=2f(x)=-2 : (a) A simplified form of the difference quotient f(x+h)f(x)h\frac{f(x+h)-f(x)}{h}, when h=0h=0, is \square (b) Use the simplified form to compute the difference quotient for the following.
When x=2x=2 and h=1h=1, the difference quotient is \square .
When x=2x=2 and h=0.2h=0.2, the difference quotient is \square .
When x=2x=2 and h=0.1h=0.1, the difference quotient is \square .
When x=2x=2 and h=0.01h=0.01, the difference quotient is \square

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Problem 149

أي من التالية يذكر مرة واحدة في البرنامج Select one: a. static method b. private method c. finalize method d. main method

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Problem 150

1. Plot Basic Linear Functions - Draw the graph of y=2x+1y=2 x+1. - Draw the graph of y=12x+3y=-\frac{1}{2} x+3 - Draw the graph of y=x4y=x-4

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Problem 151

11) if limx43x12x2mx+4\lim _{x \rightarrow 4} \frac{3 x-12}{x^{2}-m x+4} A) 3

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Problem 152

Ex5: Pour chaque fonction ci-dessous, déterminer si c'est une fonction polynôme de degré 2. 1) f(x)=x2+2x2f(x)=x^{2}+2 x-\sqrt{2} 6) w(x)=x2+9x+37w(x)=\frac{x^{2}+9 x+3}{7} 2) g(x)=2(x9)2g(x)=2(x-9)^{2} 3) h(x)=5x+9h(x)=5 x+9 7) a(x)=x2+9x+3xa(x)=x^{2}+9 x+\frac{3}{x} 4) u(x)=x2+3u(x)=x^{2}+3 5) v(x)=(5x+6)(1x)v(x)=(5 x+6)(1-x) 8) b(x)=x2+5xb(x)=x^{2}+5 \sqrt{x}

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Problem 153

5. (a) If y=3sinx+x2lnxy=3 \sin x+x^{2} \ln x, find dydx\frac{d y}{d x} (b) If x2+3y22x=x2\frac{x^{2}+3 y^{2}}{2 x}=x^{2}, find dydx\frac{d y}{d x} (c) If x=cosθ+θx=\cos \theta+\theta and y=cosθθy=\cos \theta-\theta \quad, find dy/dxd y / d x (d) Solve the equation 5x+1=2x15^{x+1}=2^{x-1}

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Problem 154

The function gg is defined by the following rule. g(x)=4x5g(x)=-4 x-5
Complete the function table. \begin{tabular}{|c|c|} \hlinexx & g(x)g(x) \\ \hline-5 & \square \\ \hline-1 & \square \\ \hline 0 & \square \\ \hline 2 & \square \\ \hline \end{tabular}

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Problem 155

3) 49(x+13x)dx\int_{4}^{9}\left(\sqrt{x}+\frac{1}{3 \sqrt{x}}\right) d x

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Problem 156

Question Watch Videc
Given the function h(x)=3x6x33h(x)=-3 x \sqrt{6 x^{3}-3}, find h(x)h^{\prime}(x) in any form.

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Problem 157

Question
Given the function y=3x2sin4(x)y=3 x^{2} \sin ^{4}(x), find dydx\frac{d y}{d x} in any form. Note: make sure to write trig functions using parentheses like sin2(x)\sin ^{2}(x) instea interpreter might not be able to understand your expression.

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Problem 158

CHALLENGE ACTIVITY 1.3.1: Spreadsheets: Formulas and functions. 5994884535568.9×35994884535568.9 \times 3 zay 7 Jump to level 1 Set B1 equal to A3 by using a formula. Hint: Start with = Feedback

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Problem 159

Challenge activities
CHALLENGE ACTIVITY 1.3.1: Spreadsheets: Formulas and functions. 599488.4535568 . qx3zay7
Jump to level 1 Set B1 equal to A1 minus A2 by using a formula. \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline[]:[-]: & & & & & & \\ \hline \\ \hline \end{tabular} 3 Check Next Eeedback?

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Problem 160

8:52 AM Sat Sep 7 4%4 \% zyBooks
Challenge activities CHALLENGE ACTIVITY 1.3.1: Spreadsheets: Formulas and functions. 599488.4535568.q×3z9y7599488.4535568 . q \times 3 z 9 y 7 Jump to level 1 Use the SUM function to set A4 to the sum of A1:A3. \begin{tabular}{|l|l|l|l|l|} \hline 1 & 2 & 3 & 4 & 5 \\ \hline \end{tabular} Check Next Feedback?

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Problem 161

learn.zybooks.com zyBooks My library > MAT 240:... > 3%3 \% 1.3: Data and spreadshe... ? Jeyna Sykes 599488.4535568.9×329y7599488.4535568 .9 \times 329 y 7 Jump to level 1
Use the SUM function to set A4 to the sum of A1:A3. \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline [-]: & & & & & \\ \hline- & A & B & C & D & E & F \\ \hline 1 & 626 & & & & \\ \hline 2 & 658 & & & & \\ \hline 3 & 133 & & & & \\ \hline 4 & & & & & \\ \hline 5 & & & & & \\ \hline 6 & & & & & \\ \hline 7 & & & & & \\ \hline 8 & & & & & \\ \hline 9 & & & & & \\ \hline 10 & & & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline 1 & 2 & 3 & 4 & 5 \\ \hline \end{tabular} Check Next Feedback? CHALLENGE ACTIVITY 1.3.2: Tables and spreadsheets. \square 5994884535568.q×3zqy75994884535568 . \mathrm{q} \times 3 \mathrm{zqy} 7 Start \square 1

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Problem 162

1. Given the function f(x)=(14)xf(x)=\left(\frac{1}{4}\right)^{x}, evaluate each of the following. (a) f(3)f(-3) (b) f(12)f\left(-\frac{1}{2}\right) (c) f(0)f(0)

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Problem 163

In Problems 9-16, use the graph of the function ff she mate the indicated limits and function values.
A 9. f(0.5)f(-0.5) Figure for 9169-16
11. f(1.75)f(1.75)
10. f(0.5)f(0.5)
13. (A) limx0f(x)\lim _{x \rightarrow 0^{-}} f(x)
12. f(2.25)f(2.25) (C) limx0f(x)\lim _{x \rightarrow 0} f(x) (B) limx0+f(x)\lim _{x \rightarrow 0^{+}} f(x)
14. (A) limx1f(x)\lim _{x \rightarrow 1^{-}} f(x) (D) f(0)f(0) (C) limx1f(x)\lim _{x \rightarrow 1} f(x) (B) limx1+f(x)\lim _{x \rightarrow 1^{+}} f(x)
15. (A) limx2f(x)\lim _{x \rightarrow 2^{-}} f(x) (D) f(1)f(1) (C) limx2f(x)\lim _{x \rightarrow 2} f(x) (B) limx2+f(x)\lim _{x \rightarrow 2^{+}} f(x)
16. (A) limx4f(x)\lim _{x \rightarrow 4^{-}} f(x) (D) f(2)f(2) (C) limx4f(x)\lim _{x \rightarrow 4} f(x) (B) limx4+f(x)\lim _{x \rightarrow 4^{+}} f(x)

In Problems 17-21 (D) f(4)f(4)

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Problem 164

Select all the rational zeros of the polynomial function. f(x)=4x37x+3f(x)=4 x^{3}-7 x+3

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Problem 165

Use the graph of f(x)f(x) in the given figure to find the following values or state that they do not exist. (a) f(3)f(3) (b) limx3f(x)\lim _{x \rightarrow 3} f(x) (c) f(0)f(0) (d) limx0f(x)\lim _{x \rightarrow 0} f(x) your choice. A. limx3f(x)=4\lim _{x \rightarrow 3} f(x)=-4 (Type an integer or a decimal.) B. The limit does not exist. (c) Find f(0)f(0). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. f(0)=5f(0)=-5 (Type an integer or a decimal.) B. f(0)f(0) is undefined. (d) Find limx0f(x)\lim _{x \rightarrow 0} f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. limx0f(x)=\lim _{x \rightarrow 0} f(x)= \square (Type an integer or a decimal.) B. The limit does not exist. me solve this View an example Get more help . Clear all Cheek answer

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Problem 166

f(x)=x213x+36x4f(x)=\frac{x^{2}-13 x+36}{x-4} (a) Explain why ff has a removable discontinuity at x=4x=4. (Select all that apply.) f(4)f(4) is undefined. f(4)f(4) and limx4f(x)\lim _{x \rightarrow 4} f(x) are finite, but are not equal. limx4f(x)\lim _{x \rightarrow 4} f(x) does not exists. limx4f(x)\lim _{x \rightarrow 4} f(x) is finite. none of the above

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Problem 167

Find the inverse function of f(x)=13+x3f(x)=13+\sqrt[3]{x} f1(x)=f^{-1}(x)= \square

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Problem 168

What is the least degree possible for the graph of the polynomial function below.

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Problem 169

Iadratic Functions Determine the equation of a quadratic funcric that satisfies each set of conditions. a) xx-intercepts 1 and 1,y-1, y-intercept 3

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Problem 170

Fill in the table using this function rule. y=10x3y=-10 x-3 \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-5 & \square \\ \hline-1 & \square \\ \hline 0 & \square \\ \hline 1 & \square \\ \hline \end{tabular}

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Problem 171

Question Express sinC\sin C as a fraction in simplest terms.
Answer Attempt 2 out of 2 sinC=\sin C= \square Submit Answer \sqrt{ } MacBook Air

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Problem 172

Given the function h(x)=(x+2)2 h(x) = (x + 2)^2 , find functions f(x) f(x) and g(x) g(x) such that h(x)=f(g(x)) h(x) = f(g(x)) .

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Problem 173

Determine the interval(s) on which the following function is continuous, then analyze the given limits. h(x)=4+4sinxcosx;limxπ/2+h(x);limx5π/3h(x)h(x)=\frac{4+4 \sin x}{\cos x} ; \lim _{x \rightarrow \pi / 2^{+}} h(x) ; \lim _{x \rightarrow 5 \pi / 3} h(x)

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Problem 174

9. Fläche zwischen Kurve und xx-Achse
Gesucht ist der Inhalt der Fläche zwischen dem Graphen von ff und der xx-Achse über dem Intervall I. Fertigen Sie eine Skizze an. a) f(x)=x+3,I=[0;4]f(x)=x+3, I=[0 ; 4] b) f(x)=2x2+1,I=[1;2]f(x)=2 x^{2}+1, I=[1 ; 2] c) f(x)=(2x)2,I=[1;3]f(x)=(2-x)^{2}, I=[1 ; 3]

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Problem 175

Determine the interval(s) on which the function f(x)=cscxf(x)=\csc x is continuous, then analyze the limits limxπ/4f(x)\lim _{x \rightarrow-\pi / 4} f(x) and limx2πf(x)\lim _{x \rightarrow 2 \pi^{-}} f(x).

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Problem 176

Points: 0 of 1 a. limx2g(x)\lim _{x \rightarrow 2} g(x) b. limx3g(x)\lim _{x \rightarrow 3} g(x) c. limx4g(x)\lim _{x \rightarrow 4} g(x) d. limx3.5g(x)\lim _{x \rightarrow 3.5} g(x) a. What is limx2g(x)\lim _{x \rightarrow 2} g(x) ? Choose the correct answer below and, if necessary, if in the arswer box to complete your choice A. limx2g(x)=\lim _{x \rightarrow 2} g(x)= \square B. limx2g(x)\lim _{x \rightarrow 2} g(x) does not exist

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Problem 177

Find the average rate of change of the function f(x)=x2x+2 f(x) = \frac{x^{2}}{x+2} over the interval [1,10][-1, 10].

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Problem 178

Write the domain and the range of the function as an inequality, using set notation, and using interval notation. Also describe the end behavior of the function or explain why there is no end behavior.
5. The graph of the quadratic function f(x)=x2+2f(x)=x^{2}+2 is shown.
6. The graph of the exponential function f(x)=3xf(x)=3^{x} is shown.

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Problem 179

Fill in the blanks for the attributes of the functions shown in the graphs below. 1. f(x)f(x) is positive on the interval \qquad f(x)f(x) has a zero at x=x= \qquad f(x)f(x) is increasing on the interval \qquad f(x)f(x) is decreasing on the interval \qquad f(x)f(x) has a local minimum of \qquad at x=x= \qquad

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Problem 180

Draw the graph of f(x)=(x1)2+4f(x)=(x-1)^{2}+4 below.
Clear All Draw: 少 ハVে

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Problem 181

8. Given the function f(x)={2x+4,0x<85x+11,x8f(x)=\left\{\begin{array}{lr} -2 x+4, & 0 \leq x<8 \\ -5 x+11, & x \geq 8 \end{array}\right. is the function increasing or decreasing over the interval [2,7][2,7] ? Find the rate of change over this interval.

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Problem 182

Let f(x)=x+2x+7f1(4)=\begin{array}{l} f(x)=\frac{x+2}{x+7} \\ f^{-1}(-4)= \end{array}

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Problem 183

compute the monthly cost for a subscriber, where xx is the number of C(x)={19.99 if 0<x2500.25x42.51 if x>250C(x)=\left\{\begin{array}{ll} 19.99 & \text { if } 0<x \leq 250 \\ 0.25 x-42.51 & \text { if } x>250 \end{array}\right.
Compute the monthly cost of the cellular phone for use of the followi (a) 150 (b) 300 (c) 251 (a) C(150)=$C(150)=\$ \square (Round to the nearest cent as needed.)

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Problem 184

\begin{tabular}{|c|c|c|} \hliney=y= & x|x| & yy is.. \\ \hlinex1x_{1} & y1\because y_{1} & \\ \hline-4 & 4 & \\ \hline-3 & 3 & \square \\ \hline - & 3 & A \ \\ \hline-2 & 2 & ・ \\ \hline-1 & 1 & \sim \sim \sim \\ \hline 0 & 0 & DNDOH \\ \hline 1 & 1 & \square \\ \hline & & +1+1+1+1 \\ \hline 2 & 2 & a+iO \\ \hline 3 & 3 & \because \\ \hline 4 & 4 & H1MMHAMM1MO \\ \hline \end{tabular} \begin{tabular}{|c|c|c|} \hline & & yy is a number squared \\ \hlinex1x_{1} & y1\because y_{1} & HHH \\ \hline-4 & 2 & \square M \\ \hline-3 & 9 & \rightarrow 的 \\ \hline-2 & - & \\ \hline-1 & 1 & 0. \\ \hline 0 & 0 & a \\ \hline 1 & 1 & \\ \hline & & - 1 - 1 - 1 \\ \hline 2 & ・ & \therefore Z \\ \hline 3 & 9 & 414-1 \\ \hline 4 & 2 & \\ \hline \end{tabular}

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Problem 185

Determine whether the function has an inverse function. f(x)=x1,x1f(x)=\sqrt{x-1}, \quad x \geq 1 Yes, ff does have an inverse. No, ff does not have an inverse.
If it does, find the inverse function. (If an answer does not exist, enter DNE.) f1(x)=f^{-1}(x)= \square x0x \geq 0

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Problem 186

Evaluate the real world polynomial. (1 point each) Charlize wants to measure the depth of an empty well. She drops a ball into the well and measures how long it takes the ball to hit the bottom of the well. She uses a stopwatch, starting when she lets go of the ball and ending when she hears the ball hit the bottom of the well. The polynomial h=16t2+6h=-16 t^{2}+6 represents how far the ball has fallen after tt seconds.
4. How far has the ball fallen after one second? -10 feet
5. Charlize's stopwatch measured a time of 3.2 seconds when the ball hit the bottom of the well. How deep is the well?

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Problem 187

Indicate graph function r(x)=4x2 r(x) = -4x^2

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Problem 188

Find the average rate of change of the function y=2x2+2x+1 y = 2x^2 + 2x + 1 on the interval 2x5 2 \leq x \leq 5 .

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Problem 189

Let f(x)=2xf(x)=2 \sqrt{x} If g(x)g(x) is the graph of f(x)f(x) shifted up 1 units and right 5 units, write a formula for g(x)g(x). g(x)=g(x)=

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Problem 190

Given that g(x)=3x24x+2\mathrm{g}(\mathrm{x})=3 \mathrm{x}^{2}-4 \mathrm{x}+2, find each of the following. a) g(0)g(0) b) g(2)g(-2) c) g(3)g(3) d) g(x)g(-x) e) g(1t)g(1-t)

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Problem 191

Find the domain of the following function. Do not use a g f(x)=1x22x3f(x)=\frac{1}{x^{2}-2 x-3}
The domain is \square (Type your answer in interval notation.)

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Problem 192

Evaluate the function f(x)=x2+4x4f(x)=x^{2}+4 x-4 at the given values of the independent variable and simplify a. f(2)f(-2) b. f(x+7)f(x+7) c. f(x)f(-x) a. f(2)=f(-2)= \square (Simplify your answer.) b. f(x+7)=f(x+7)= \square (Simplify your answer) c. f(x)=f(-x)=\square \square (Simplify your answer)

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Problem 193

Evaluate the function f(x)=x2+4x4f(x)=x^{2}+4 x-4 at the given values of the independent variable and simplify a. f(2)f(-2) b. f(x+7)f(x+7) c. f(x)f(-x) a. f(2)=f(-2)=\square \square (Simplify your answer.) b. f(x+7)=f(x+7)= \square (Simplify your answer) c. f(x)=f(-x)= \square (Simplify your answer)

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Problem 194

Example 4.16 Sketch the graph of each of the following functi Hence, state its domain and range. (a) f(x)=3x+1f(x)=3^{x+1}. (b) f(x)=3x1f(x)=3^{x}-1. (c) f(x)=3x+1f(x)=3^{x}+1 (d) f(x)=3xf(x)=3^{x}. (e) f(x)=(14)x+1f(x)=\left(\frac{1}{4}\right)^{x+1} (f) f(x)=(14)x1f(x)=\left(\frac{1}{4}\right)^{x}-1 (g) f(x)=(14)x+1f(x)=-\left(\frac{1}{4}\right)^{x}+1 (h) f(x)=(14)x+1f(x)=-\left(\frac{1}{4}\right)^{x+1}

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Problem 195

9. f(x)=11+x2f(x)=\frac{1}{1+x^{2}} бол f(x),f(x3),f(1x),2f(x),14f(x)+5f(1x)f(-x), f(x-3), f\left(\frac{1}{x}\right), 2 f(x), \frac{1}{4} f(x)+5 f\left(\frac{1}{x}\right)-ийг ол.

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Problem 196

10. 6o. - thin f(x)=3x+132x2f(x)=\frac{3 x+1}{3-2 x^{2}} бол f(1x)f(1-x)-ийг ол.

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Problem 197

Listen The Period of both y=sinxy=\sin x and y=cosxy=\cos x is π\pi. True False Submit Quiz 4 of 5 questions saved MacBook Pro

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Problem 198

Suraj took a slice of pizza from the freezer and put it in the oven. The pizza was heated at a constant rate.
The table compares the pizza's temperature (in degrees Celsius) and the time since Suraj started heating it (in minutes). \begin{tabular}{c|c|} \hline Time (minutes) & Temperature (degrees Celsius) \\ \hline 4 & 25 \\ 6 & 40 \\ 8 & 55 \\ \hline \end{tabular}
How long did it take the pizza to reach 100 degrees Celsius? \square minutes

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Problem 199

The price of a train ticket consists of an initial fee plus a constant fee per stop.
The table compares the number of stops and the price of a ticket (in dollars). \begin{tabular}{cc} Stops & Price (dollars) \\ \hline 3 & 6.50 \\ 7 & 12.50 \\ 11 & 18.50 \end{tabular}
What is the fee per stop? \$

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Problem 200

Find the following for the given functions. f(x)=xx+6g(x)=x3f(x)=\frac{x}{x+6} g(x)=x^{3} (a) (f+g)(x)=(f+g)(x)= \square (b) (fg)(x)=(f-g)(x)= \square (c) (fg)(x)=(f g)(x)= \square (d) (fg)(x)=\left(\frac{f}{g}\right)(x)= \square
What is the domain of fg\frac{f}{g} ? (Enter your answer using interval notation.) \square Need Help? Read it Watchit Submit Answer Need Help? 14. [-/3 Points] DETAILS MY NOTES LARPCALC11 1.8.019. Evaluate the function for f(x)=x+3f(x)=x+3 and g(x)=x22g(x)=x^{2}-2. (fg)(7)(fg)(7)=\begin{array}{c} (f g)(7) \\ (f g)(7)=\square \end{array} Need Help? Read it Submit Answer

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