Function

Problem 3501

If $x + \frac{1}{x} = 5$ , find $x^3 + \frac{1}{x^3}$ .

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Problem 3502

Create an expression: add $n$ and 2, then add 9 to that result. Do not simplify.

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Problem 3503

Create an expression: double $p$ and then add $q$ to it, without simplifying.

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Problem 3504

Does the function $f(x)=x$ have a limit as $x$ approaches 3 from all real numbers except 3?

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Problem 3505

Write the expression: subtract $s$ from $r$ , add $q$ , then triple the result. Don't simplify.

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Problem 3506

Simplify the function $f(x)=\frac{x}{x}$ .

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Problem 3507

Create an expression for: divide 2 by $a$ , then triple the result. Do not simplify.

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Problem 3508

Maximize $P=3x + 2y$ with constraints: $5x + y \leq 16$ , $2x + 3y \leq 22$ , $x \geq 0$ , $y \geq 0$ .

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Problem 3509

Translate the function $f(x)=2x-6$ by moving it 3 units up.

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Problem 3510

Find the function $g$ that represents the graph of $f(x)=2x-8$ translated 5 units to the right.

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Problem 3511

Find the reflection of the function $f(x)=|2x|+2$ across the $x$ -axis.

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Problem 3512

Stretch the function $f(x)=3x+9$ horizontally by a factor of 4.

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Problem 3513

Reflect the function $f(x)=\frac{1}{5} x+6$ in the $y$ -axis. What is the new function?

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Problem 3514

Transform $f(x)=|x+4|$ with a horizontal shrink by a factor of $\frac{1}{5}$ .

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Problem 3515

Translate $f(x)=|x|$ 4 units right and then reflect it.

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Problem 3516

Shannon has job offers: Company ABC: \$45,500 with 8\% raise yearly; Company XYZ: \$62,000 with 3\% raise. After 15 years, which is better?

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Problem 3517

Graph the function $y=x^{3}$ .

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Problem 3518

A freight elevator starts with 15,893 lbs, adds 3,473 lbs, then removes 5,492 lbs. Find the weight $w$ using the right equation.
Options: $w=15,893-3,473+5,492$ $w=15,893-3,473-5,492$ $w=15,893+3,473-5,492$ $w=15,893+3,473+5,492$

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Problem 3519

Identify a value from the range of function $A$ given the pairs: $(-1, 1)$ , $(-2, 2)$ , $(-3, 3)$ , $(-4, 4)$ , $(-5, 5)$ .

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Problem 3520

Identify the parent function for the equation $f(x)=-14+3$ .

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Problem 3521

A ball is thrown with a velocity of $41 \mathrm{ft/s}$ . Its height after $t$ seconds is $y=41t-22t^2$ . Find average velocity for $t=2$ over 0.01, 0.005, 0.002, and 0.001 seconds, then determine instantaneous velocity at $t=2$ .

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Problem 3522

A ball is thrown with a velocity of $41 \mathrm{ft/s}$ . Its height is $y=41t-22t^2$ . Find average velocity from $t=2$ for given intervals and the instantaneous velocity at $t=2$ .

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Problem 3523

What type of transformation occurs when all outputs of a parent function are increased by 5?

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Problem 3524

Find the average rate of change of the function $f(x)=x^{2}+6x+10$ over the interval $[-2,1]$ .

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Problem 3525

Sketch a function with a negative average rate of change on the interval $[0,3]$ .

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Problem 3526

Find the zeros and their multiplicities for the function $y=4 x^{3}(x+2)^{3}(x+1)$ .

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Problem 3527

Find the zeros and their multiplicities for the function: $y=4 x^{3}(x+2)^{3}(x+1)$ .

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Problem 3528

Find the degree of the function $f(x) = 2 x^{3} - 1$ . Options: 3, 2, 1, 0.

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Problem 3529

Graph the transformed function $y=\frac{1}{3} \sqrt{x}$ based on its parent function.

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Problem 3530

¿Qué calificación mínima necesita el estudiante en el parcial 3 (30\%) para aprobar con 3.0, dado sus otros resultados?

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Problem 3531

10 times 8 hundreds equals 8; solve: $10 \times 800 = x$ and $8,000 = 10x$ .

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Problem 3532

Given the pairs, find $g(3)$ from $g(x):\{(0,5),(3,4),(5,3)\}$ .

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Problem 3533

Determine if the function $f(x)=x^{5}-2x^{3}$ is even, odd, or neither algebraically.

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Problem 3534

Determine if the function $q(x)=x^{3}+2 x^{2}-1$ is even, odd, or neither.

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Problem 3535

Graphically analyze if the function $g(x)=x^{3}-x$ is even, odd, or neither.

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Problem 3536

Determine if the function $g(x)=x^{3}-x$ is even, odd, or neither.

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Problem 3537

Determine if the function $h(x)=x^{2}+1$ is even, odd, or neither using algebraic methods.

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Problem 3538

John earns $\$ 8.50$ per hour for up to 40 hours weekly. Explain $P(25)=212.5$ and state the domain & range.

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Problem 3539

A ball's height after $t$ seconds is $h(t)=144t-16t^{2}$ . What does $h(2)=224$ mean?

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Problem 3540

Mary types 65 words/min for 30 min, $T(x)=65x$ . Interpret $P(25)=1625$ and find the domain and range.

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Problem 3541

Malik has a \ $50 gift card for movies costing \$6 each. Write a sequence rule and find how many movies he can see.$ $f(x)=$ $ Malik can see movies to deplete the card.

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Problem 3542

A cab driver charges \ $4 per mile. The meter shows \$7.50 for 2 miles, \$11 for 3 miles. Find fares for 4, 5, 6 miles.$ $f(4)=$ $f(5)=$ $f(6)=$ $ Also, write a recursive rule for this fare structure.

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Problem 3543

A cab charges \ $4 per mile, with an arithmetic fare. Find fares for 4, 5, and 6 miles:$ \mathrm{f}(4) $,$ \mathrm{f}(5) $,$ \mathrm{f}(6)$. Write a recursive rule.

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Problem 3544

What equation calculates the total weight $t$ of a firefighter weighing $x$ pounds and 60 pounds of equipment?

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Problem 3545

If Ram earns 20% more than Hari, what percent less is Hari's income than Ram's? Options: (a) 16 2/3% (b) 20% (c) 23 1/3% (d) 17% (e) None.

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Problem 3546

If sugar prices rise by $25\%$ , by how much must a lady reduce her consumption to keep spending the same? (a) $25\%$ (b) $20\%$ (c) $30\%$ (d) None of these

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Problem 3547

If $x \Rightarrow y$ and $y \Rightarrow z$ , which must be true: A. $z \Rightarrow x$ , B. $\neg x \Rightarrow z$ , C. $\neg x \Rightarrow \neg z$ , D. $x \Rightarrow z$ ?

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Problem 3548

Calculate the molarity (c) of a solution with osmotic pressure $\pi = 13$ atm and temperature $T = 395$ K using $\pi = cRT$ .

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Problem 3549

Calculate the new gravitational force when two objects, initially 1000 N apart at distance D, are separated by D/4.

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Problem 3550

The population function is $p(t)=0.4t+28.2$ . Which statement about the town's population growth is true? A) B) C) D)

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Problem 3551

Graph the piecewise function: $f(x)=\begin{cases} 3, & -\infty<x\leq-1 \\ x-3, & -1<x\leq2 \\ x/2, & 2<x\leq\infty \end{cases}$

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Problem 3552

Identify the expression for "half the sum of 10 and a number": $\frac{1}{2}(10+x)$ , $\frac{1}{2}(10)+x$ , $\frac{1}{2} x+10$ , $\frac{1}{2}+10+x$ .

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Problem 3553

Given the piecewise function $f(x)$ , find: a. $f(-2)$ , b. $f\left(-\frac{2}{5}\right)$ , c. $f(4)$ , d. $x$ if $f(x)=-2.5$ .

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Problem 3554

Identify the components of the cost expression $180 + 15x$ for a soccer goal and balls. What does each part represent?

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Problem 3555

Monique buys a baseball for \$20, a soccer ball for \$15, and tennis balls for \$12. What is the price after tennis ball discount?
$12(1-y)$

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Problem 3556

The Garza family's distance to the park is $315-55h$ . What do $315$ , $55$ , and $h$ represent?

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Problem 3557

Identify the components of the expression $60 + 20x$ for the total cost: jeans, shirts, $60$ , $20$ , and $20x$ .

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Problem 3558

What is the cost of the tennis balls after applying a discount of $y$ percent? Options: $20+15+12$ , $12(1-y)$ , $20(1-x)$ , 12.

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Problem 3559

Find the limit as $x$ approaches 0 for the expression $\frac{\sin x}{x}$ .

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Problem 3560

Can a car with 30 mpg and a 20-gallon tank drive 252 miles without refueling?

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Problem 3561

Bestimme die Funktionsgleichung $f(x)=c \cdot a^{x}$ durch die Punkte P und Q. Für welches $x$ gilt $f(x)=256$ ? a) $P(0 \mid 4)$ , $Q(4 \mid 0,5)$ b) $P(0 \mid 0,25)$ , $Q(6 \mid 16)$ c) $P(0 \mid 512)$ , $Q(-3 \mid 8)$

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Problem 3562

Find values for the piecewise function $f(x)$ : a. $f(-2)$ b. $f\left(-\frac{2}{5}\right)$ c. $f(4)$ d. Solve $f(x)=-2.5$ .

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Problem 3563

Find where the polynomial $y=x^{2}+3x+2$ intersects the $y$ -axis.

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Problem 3564

Find the end behavior of $y$ as $x \to \infty$ for the equation $y = -7x^{3}$ .

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Problem 3565

Last year $k$ pies were baked, this year 196. Write an expression for total pies over two years: $k + 196$ .

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Problem 3566

Determine the end behavior of $y$ as $x \to -\infty$ for the equation $y=-4x^{5}+4x^{2}-8$ .

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Problem 3567

Calculate the value of $\cos 45^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

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Problem 3568

Find if the average cost per patient per day, given by $\frac{72.453 x^{2}+1354.5 x+2196.5}{x+4}$ , will reach \ $4000 by 2026. What is$ x $?$ $x=$ $

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Problem 3569

Find if average hospital cost per patient per day will reach \ $4000 by 2026 using$ x=26$. A. Yes B. No.

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Problem 3570

Find the second quarter revenue for 2015 using the model $8.63 x^{0.524}$ with $x=10$ . What is $x$ ?
$x=$

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Problem 3571

Find the exact value of $\tan 45^{\circ}$ . What is $\tan 45^{\circ}=$ ? Simplify your answer.

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Problem 3572

Use the rule $y=4x+5$ to find $y$ values for $x=1, 2, 4, 7$ . Fill in the table with these results.

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Problem 3573

Use the function $y=2x-1$ to find $y$ for $x=2, 5, 6, 7$ . Fill in the missing values.

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Problem 3574

Calculate the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{4 x}{x+3}$ , where $h \neq 0$ .

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Problem 3575

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3}{x^{2}}$ , where $h \neq 0$ .

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Problem 3576

Express the gross salary $G$ for someone earning \ $26/hour as a function of hours worked$ x $. What is$ G(x)$?

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Problem 3577

Find the perimeter $\mathrm{P}$ of a rectangle as a function of width $\mathrm{W}$ , given length is $2\mathrm{W}$ .

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Problem 3578

An airplane flies 3000 miles at 500 mph. Cost per passenger is $C(x)=75+\frac{x}{25}+\frac{31,000}{x}$ . Find cost with no wind. $\$ \square$ (Round to the nearest cent.)

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Problem 3579

An airplane crosses 3000 miles at 500 mph. Find cost $C(x)=75+\frac{x}{25}+\frac{31,000}{x}$ per passenger for: (b) headwind 50 mph: \$161.89; (c) tailwind 100 mph: \$\square.

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Problem 3580

An airplane flies 3000 miles at 500 mph. Cost per passenger is $C(x)=75+\frac{x}{25}+\frac{31,000}{x}$ . Find costs for 100 mph tailwind and headwind.

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Problem 3581

An airplane flies 3000 miles at 500 mph. Cost per passenger is $C(x)=75+\frac{x}{25}+\frac{31,000}{x}$ . Find costs for no wind and 50 mph headwind.

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Problem 3582

Revenue from selling $x$ hundred cell phones is $R(x)=-1.9x^2+323x$ . Cost is $C(x)=0.09x^3-2x^2+75x+600$ . Find profit $P(x)=R(x)-C(x)$ , then compute $P(25)$ . Interpret $P(25)$ .

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Problem 3583

Given revenue $R(x)=-1.9 x^{2}+323 x$ and cost $C(x)=0.09 x^{3}-2 x^{2}+75 x+600$ :
(a) Find profit $P(x)=R(x)-C(x)$ .
(b) Calculate profit for $x=25$ hundred phones.
(c) Explain $P(25)$ .

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Problem 3584

Find $y$ using the formula $y=m x$ for $m=8$ and $x=7$ .

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Problem 3585

The function $f$ is shown below. If $g$ is the function defined by $g(x)=\int_{-2}^{x} f(t) d t$ , what is the value of $g(9)$ ?

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Problem 3586

Graph the given functions, f and g , in the same rectangular coordinate system. Then describe how the graph of g is related to the graph of f. $\begin{array}{l} f(x)=x \\ g(x)=x-6 \end{array}$
Use the graphing tool to graph the functions.
How is the graph of f shifted to get the graph of g ? The graph of g is the graph of f shifted $\square$ by $\square$ units.

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Problem 3587

Graphing Functions Using Vertical and Horizontal Shifts
For each of the following, fill in the blanks to describe how the graph of the function is a transformation of the graph of the original function. (Enter a positive number in each first blank, and indicate the correct direction from the dropdown menu.) a. $y=f(x-4)-9$
The function $f$ has been shifted: horizontally $\square$ units $\square$ ? and vertically $\square$ units $\square$ ? . b. $y=g(x+5)+1$
The function $g$ has been shifted: horizontally $\square$ units $\square$ , and vertically $\square$ units $\square$ ? .
For additional help with this problem type, access the following resources: - TEXT Read College Algebra with Corequisite Support 2e 3.5 Transformation of Functions of the text.

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Problem 3588

```latex At every point along the AFC curve in the figure to the right, what is true of the dollar amount of this firm's total fixed costs at any given point that one might select?
Total fixed cost is $\square$ by definition. If the output rate is 250 units in the figure, then AFC equals \\square $per unit so that TFC equals \$$ \square $. It follows then that, if 314 units are produced per time period, AFC must equal \$$ \square$ per unit. (Enter your responses rounded to two decimal places.) ```

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Problem 3589

Graph the given functions, f and g , in the same rectangular coordinate system. Describe how the graph of g is related to the graph of f . $\begin{array}{l} f(x)=x^{3} \\ g(x)=x^{3}+2 \end{array}$
Use the graphing tool to graph the functions. $\square$ How is the graph of $g$ related to the graph of $f$ ?

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Problem 3590

The function $g(x)=3.2 \sqrt{x}+9.8$ models the median height, $g(x)$ , in inches, of children who are $x$ months of age. The graph of g is shown.
The median height is 25.5 inches. (Round to the nearest tenth of an inch.) The actual median height for children at 24 months is 25 inches. How well does the model describe the actual height?
The model describes the actual height A. very well. B. poorly. c. Use the model to find the average rate of change, in inches per month, between birth and 10 months.
The average rate of change is 1.0 inches per month. (Round to the nearest tenth.) d. Use the model to find the average rate of change, in inches per month, between 40 and 50 months.
The average rate of change is 0.2 inches per month. (Round to the nearest tenth.)
How does this compare with your answer in part (c)? How is this difference shown by the graph? A. The average rate of change is smaller. The graph is not as steep. B. The average rate of change is smaller. The graph is steeper. C. The average rate of change is larger. The graph is steeper. D. The average rate of change is larger. The graph is not as steep.

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Problem 3591

Find the the domain of the function $f(x)=\frac{x-9}{x^{2}+7 x-30}$ . $\{x \mid x \neq 30\}$ $\{x \mid x \neq-30\}$ $\{x \mid x \neq-9\}$

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Problem 3592

Question 1 (Multiple Choice Worth 5 points) (02.07 MC)
Given a function $f(x)=2 x^{2}+3$ , what is the average rate of change of $f$ on the interval $[2,2+h] ?$ 11 $2 h+8$ $2 h^{2}+8 h$ $2 h^{2}+8 h+11$

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Problem 3593

Question 29
Given the function defined by $f(x)=7 x-2$ , find $f(-5)$ . Simplify. $f(-5)=$ $\square$

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Problem 3594

Relatel Ratas
17. The volume of a cube decreases at a rate of $10 \mathrm{~m}^{3} / \mathrm{s}$ . Find the rate at which the side of the cube changes when the side of the cube is 2 m .

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Problem 3595

For $f(x)=-4 x+5$ , find each value. Progress: 0/2
Part 1 of 2 (a) $f(5)+2=$

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Problem 3596

Given the function defined by $g(x)=-x^{2}+3 x+3$ , find $g(-2)$ . Simplify. $g(-2)=$ $\square$

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Problem 3597

Given the function defined by $g(x)=3 x^{2}-7 x+3$ , find $g(-2 x)$ . Express the answer in simplest form. $g(-2 x)=$

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Problem 3598

4. Determine the domain of $f(x)=\sqrt[n]{a x+b}$ , where $n$ is an odd positive integer. a) $x \geq-\frac{b}{a}$ b) $x \geq \frac{b}{a}$ c) $-\frac{b}{a} \leq x \leq \frac{b}{a}$ d) all real numbers

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Problem 3599

10. Determine the range of $f(x)-3=-2 \sqrt{1-x}$ a) $y \leq-2$ b) $y \leq 1$ c) $y \leq 2$ d) $y \leq 3$

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Problem 3600

rational functions. $y=\frac{x^{2}-16}{x^{2}+2 x-3}$
If any of the following is none. Type none.
Vertical Asymptote/s: x or y $\square$ $\square$ and $\square$
Horizontal Asymptote/s: x or y $\square$ $\square$
Hole/s in the graph: $x$ or $y$ $\square$ $\square$
Domain all reals except: $\square$ and $\square$

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1 ...33 34 35 36 37 38 39 ...103

Function

Problem 3501

If x+1x=5x + \frac{1}{x} = 5x+x1​=5, find x3+1x3x^3 + \frac{1}{x^3}x3+x31​.

Problem 3502

Create an expression: add nnn and 2, then add 9 to that result. Do not simplify.

Problem 3503

Create an expression: double ppp and then add qqq to it, without simplifying.

Problem 3504

Does the function f(x)=xf(x)=xf(x)=x have a limit as xxx approaches 3 from all real numbers except 3?

Problem 3505

Write the expression: subtract sss from rrr, add qqq, then triple the result. Don't simplify.

Problem 3506

Simplify the function f(x)=xxf(x)=\frac{x}{x}f(x)=xx​.

Problem 3507

Create an expression for: divide 2 by aaa, then triple the result. Do not simplify.

Problem 3508

Maximize P=3x+2yP=3x + 2yP=3x+2y with constraints: 5x+y≤165x + y \leq 165x+y≤16, 2x+3y≤222x + 3y \leq 222x+3y≤22, x≥0x \geq 0x≥0, y≥0y \geq 0y≥0.

Problem 3509

Translate the function f(x)=2x−6f(x)=2x-6f(x)=2x−6 by moving it 3 units up.

Problem 3510

Find the function ggg that represents the graph of f(x)=2x−8f(x)=2x-8f(x)=2x−8 translated 5 units to the right.

Problem 3511

Find the reflection of the function f(x)=∣2x∣+2f(x)=|2x|+2f(x)=∣2x∣+2 across the xxx-axis.

Problem 3512

Stretch the function f(x)=3x+9f(x)=3x+9f(x)=3x+9 horizontally by a factor of 4.

Problem 3513

Reflect the function f(x)=15x+6f(x)=\frac{1}{5} x+6f(x)=51​x+6 in the yyy-axis. What is the new function?

Problem 3514

Transform f(x)=∣x+4∣f(x)=|x+4|f(x)=∣x+4∣ with a horizontal shrink by a factor of 15\frac{1}{5}51​.

Problem 3515

Translate f(x)=∣x∣f(x)=|x|f(x)=∣x∣ 4 units right and then reflect it.

Problem 3516

Shannon has job offers: Company ABC: \$45,500 with 8\% raise yearly; Company XYZ: \$62,000 with 3\% raise. After 15 years, which is better?

Problem 3517

Graph the function y=x3y=x^{3}y=x3.

Problem 3518

Problem 3519

Identify a value from the range of function AAA given the pairs: (−1,1)(-1, 1)(−1,1), (−2,2)(-2, 2)(−2,2), (−3,3)(-3, 3)(−3,3), (−4,4)(-4, 4)(−4,4), (−5,5)(-5, 5)(−5,5).

Problem 3520

Identify the parent function for the equation f(x)=−14+3f(x)=-14+3f(x)=−14+3.

Problem 3521

A ball is thrown with a velocity of 41ft/s41 \mathrm{ft/s}41ft/s. Its height after ttt seconds is y=41t−22t2y=41t-22t^2y=41t−22t2. Find average velocity for t=2t=2t=2 over 0.01, 0.005, 0.002, and 0.001 seconds, then determine instantaneous velocity at t=2t=2t=2.

Problem 3522

A ball is thrown with a velocity of 41ft/s41 \mathrm{ft/s}41ft/s. Its height is y=41t−22t2y=41t-22t^2y=41t−22t2. Find average velocity from t=2t=2t=2 for given intervals and the instantaneous velocity at t=2t=2t=2.

Problem 3523

What type of transformation occurs when all outputs of a parent function are increased by 5?

Problem 3524

Find the average rate of change of the function f(x)=x2+6x+10f(x)=x^{2}+6x+10f(x)=x2+6x+10 over the interval [−2,1][-2,1][−2,1].

Problem 3525

Sketch a function with a negative average rate of change on the interval [0,3][0,3][0,3].

Problem 3526

Find the zeros and their multiplicities for the function y=4x3(x+2)3(x+1)y=4 x^{3}(x+2)^{3}(x+1)y=4x3(x+2)3(x+1).

Problem 3527

Find the zeros and their multiplicities for the function: y=4x3(x+2)3(x+1)y=4 x^{3}(x+2)^{3}(x+1)y=4x3(x+2)3(x+1).

Problem 3528

Find the degree of the function f(x)=2x3−1f(x) = 2 x^{3} - 1f(x)=2x3−1. Options: 3, 2, 1, 0.

Problem 3529

Graph the transformed function y=13xy=\frac{1}{3} \sqrt{x}y=31​x​ based on its parent function.

Problem 3530

¿Qué calificación mínima necesita el estudiante en el parcial 3 (30\%) para aprobar con 3.0, dado sus otros resultados?

Problem 3531

10 times 8 hundreds equals 8; solve: 10×800=x10 \times 800 = x10×800=x and 8,000=10x8,000 = 10x8,000=10x.

Problem 3532

Given the pairs, find g(3)g(3)g(3) from g(x):{(0,5),(3,4),(5,3)}g(x):\{(0,5),(3,4),(5,3)\}g(x):{(0,5),(3,4),(5,3)}.

Problem 3533

Determine if the function f(x)=x5−2x3f(x)=x^{5}-2x^{3}f(x)=x5−2x3 is even, odd, or neither algebraically.

Problem 3534

Determine if the function q(x)=x3+2x2−1q(x)=x^{3}+2 x^{2}-1q(x)=x3+2x2−1 is even, odd, or neither.

Problem 3535

Graphically analyze if the function g(x)=x3−xg(x)=x^{3}-xg(x)=x3−x is even, odd, or neither.

Problem 3536

Determine if the function g(x)=x3−xg(x)=x^{3}-xg(x)=x3−x is even, odd, or neither.

Problem 3537

Determine if the function h(x)=x2+1h(x)=x^{2}+1h(x)=x2+1 is even, odd, or neither using algebraic methods.

Problem 3538

John earns $8.50\$ 8.50$8.50 per hour for up to 40 hours weekly. Explain P(25)=212.5P(25)=212.5P(25)=212.5 and state the domain & range.

Problem 3539

A ball's height after ttt seconds is h(t)=144t−16t2h(t)=144t-16t^{2}h(t)=144t−16t2. What does h(2)=224h(2)=224h(2)=224 mean?

Problem 3540

Mary types 65 words/min for 30 min, T(x)=65xT(x)=65xT(x)=65x. Interpret P(25)=1625P(25)=1625P(25)=1625 and find the domain and range.

If $x + \frac{1}{x} = 5$ , find $x^3 + \frac{1}{x^3}$ .

Create an expression: add $n$ and 2, then add 9 to that result. Do not simplify.

Create an expression: double $p$ and then add $q$ to it, without simplifying.

Does the function $f(x)=x$ have a limit as $x$ approaches 3 from all real numbers except 3?

Write the expression: subtract $s$ from $r$ , add $q$ , then triple the result. Don't simplify.

Simplify the function $f(x)=\frac{x}{x}$ .

Create an expression for: divide 2 by $a$ , then triple the result. Do not simplify.

Maximize $P=3x + 2y$ with constraints: $5x + y \leq 16$ , $2x + 3y \leq 22$ , $x \geq 0$ , $y \geq 0$ .

Translate the function $f(x)=2x-6$ by moving it 3 units up.

Find the function $g$ that represents the graph of $f(x)=2x-8$ translated 5 units to the right.

Find the reflection of the function $f(x)=|2x|+2$ across the $x$ -axis.

Stretch the function $f(x)=3x+9$ horizontally by a factor of 4.

Reflect the function $f(x)=\frac{1}{5} x+6$ in the $y$ -axis. What is the new function?

Transform $f(x)=|x+4|$ with a horizontal shrink by a factor of $\frac{1}{5}$ .

Translate $f(x)=|x|$ 4 units right and then reflect it.

Graph the function $y=x^{3}$ .

Identify a value from the range of function $A$ given the pairs: $(-1, 1)$ , $(-2, 2)$ , $(-3, 3)$ , $(-4, 4)$ , $(-5, 5)$ .

Identify the parent function for the equation $f(x)=-14+3$ .

A ball is thrown with a velocity of $41 \mathrm{ft/s}$ . Its height after $t$ seconds is $y=41t-22t^2$ . Find average velocity for $t=2$ over 0.01, 0.005, 0.002, and 0.001 seconds, then determine instantaneous velocity at $t=2$ .

A ball is thrown with a velocity of $41 \mathrm{ft/s}$ . Its height is $y=41t-22t^2$ . Find average velocity from $t=2$ for given intervals and the instantaneous velocity at $t=2$ .

Find the average rate of change of the function $f(x)=x^{2}+6x+10$ over the interval $[-2,1]$ .

Sketch a function with a negative average rate of change on the interval $[0,3]$ .

Find the zeros and their multiplicities for the function $y=4 x^{3}(x+2)^{3}(x+1)$ .

Find the zeros and their multiplicities for the function: $y=4 x^{3}(x+2)^{3}(x+1)$ .

Find the degree of the function $f(x) = 2 x^{3} - 1$ . Options: 3, 2, 1, 0.

Graph the transformed function $y=\frac{1}{3} \sqrt{x}$ based on its parent function.

10 times 8 hundreds equals 8; solve: $10 \times 800 = x$ and $8,000 = 10x$ .

Given the pairs, find $g(3)$ from $g(x):\{(0,5),(3,4),(5,3)\}$ .

Determine if the function $f(x)=x^{5}-2x^{3}$ is even, odd, or neither algebraically.

Determine if the function $q(x)=x^{3}+2 x^{2}-1$ is even, odd, or neither.

Graphically analyze if the function $g(x)=x^{3}-x$ is even, odd, or neither.

Determine if the function $g(x)=x^{3}-x$ is even, odd, or neither.

Determine if the function $h(x)=x^{2}+1$ is even, odd, or neither using algebraic methods.

John earns $\$ 8.50$ per hour for up to 40 hours weekly. Explain $P(25)=212.5$ and state the domain & range.

A ball's height after $t$ seconds is $h(t)=144t-16t^{2}$ . What does $h(2)=224$ mean?

Mary types 65 words/min for 30 min, $T(x)=65x$ . Interpret $P(25)=1625$ and find the domain and range.

A cab charges \ $4 per mile, with an arithmetic fare. Find fares for 4, 5, and 6 miles:$ \mathrm{f}(4) $,$ \mathrm{f}(5) $,$ \mathrm{f}(6)$. Write a recursive rule.

What equation calculates the total weight $t$ of a firefighter weighing $x$ pounds and 60 pounds of equipment?

If sugar prices rise by $25\%$ , by how much must a lady reduce her consumption to keep spending the same? (a) $25\%$ (b) $20\%$ (c) $30\%$ (d) None of these

If $x \Rightarrow y$ and $y \Rightarrow z$ , which must be true: A. $z \Rightarrow x$ , B. $\neg x \Rightarrow z$ , C. $\neg x \Rightarrow \neg z$ , D. $x \Rightarrow z$ ?

Calculate the molarity (c) of a solution with osmotic pressure $\pi = 13$ atm and temperature $T = 395$ K using $\pi = cRT$ .

The population function is $p(t)=0.4t+28.2$ . Which statement about the town's population growth is true? A) B) C) D)

Graph the piecewise function: $f(x)=\begin{cases} 3, & -\infty<x\leq-1 \\ x-3, & -1<x\leq2 \\ x/2, & 2<x\leq\infty \end{cases}$

Identify the expression for "half the sum of 10 and a number": $\frac{1}{2}(10+x)$ , $\frac{1}{2}(10)+x$ , $\frac{1}{2} x+10$ , $\frac{1}{2}+10+x$ .

Given the piecewise function $f(x)$ , find: a. $f(-2)$ , b. $f\left(-\frac{2}{5}\right)$ , c. $f(4)$ , d. $x$ if $f(x)=-2.5$ .

Identify the components of the cost expression $180 + 15x$ for a soccer goal and balls. What does each part represent?

Monique buys a baseball for \$20, a soccer ball for \$15, and tennis balls for \$12. What is the price after tennis ball discount?
$12(1-y)$

The Garza family's distance to the park is $315-55h$ . What do $315$ , $55$ , and $h$ represent?

Identify the components of the expression $60 + 20x$ for the total cost: jeans, shirts, $60$ , $20$ , and $20x$ .

What is the cost of the tennis balls after applying a discount of $y$ percent? Options: $20+15+12$ , $12(1-y)$ , $20(1-x)$ , 12.

Find the limit as $x$ approaches 0 for the expression $\frac{\sin x}{x}$ .

Find values for the piecewise function $f(x)$ : a. $f(-2)$ b. $f\left(-\frac{2}{5}\right)$ c. $f(4)$ d. Solve $f(x)=-2.5$ .

Find where the polynomial $y=x^{2}+3x+2$ intersects the $y$ -axis.

Find the end behavior of $y$ as $x \to \infty$ for the equation $y = -7x^{3}$ .

Last year $k$ pies were baked, this year 196. Write an expression for total pies over two years: $k + 196$ .

Determine the end behavior of $y$ as $x \to -\infty$ for the equation $y=-4x^{5}+4x^{2}-8$ .

Calculate the value of $\cos 45^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

Find if the average cost per patient per day, given by $\frac{72.453 x^{2}+1354.5 x+2196.5}{x+4}$ , will reach \ $4000 by 2026. What is$ x $?$ $x=$ $

Find if average hospital cost per patient per day will reach \ $4000 by 2026 using$ x=26$. A. Yes B. No.

Find the second quarter revenue for 2015 using the model $8.63 x^{0.524}$ with $x=10$ . What is $x$ ?
$x=$

Find the exact value of $\tan 45^{\circ}$ . What is $\tan 45^{\circ}=$ ? Simplify your answer.

Use the rule $y=4x+5$ to find $y$ values for $x=1, 2, 4, 7$ . Fill in the table with these results.

Use the function $y=2x-1$ to find $y$ for $x=2, 5, 6, 7$ . Fill in the missing values.

Calculate the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{4 x}{x+3}$ , where $h \neq 0$ .