Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(2, 5), (3, 6), (2, 7), (4, 8)\}$$

Question 2

Given $$f(x) = x^2$ + 3x - 2$$, what is $$f(-2)$$?

Accepted Answer

$$-4$$

Question 3

Find the domain of the function $$f(x) = \sqrt{13 - x}.$$

Accepted Answer

$$(-\infty, 13]$$

Question 4

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$x = y + 2$$

Question 5

Given $$f(x) = 3x^2$ - 5x - 5$$, find $$f(x-1).$$

Accepted Answer

$$3(x-1)^2 - 5(x-1) - 5$

Question 6

For the function $$g(x) = \dfrac{2x}{x^2$ - 9}$$, what is the domain?

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 7

Which of the following best describes the symmetry of the graph $$y = x^3$?

Accepted Answer

Symmetric with respect to the origin

Question 8

Determine whether the function $$f(x) = 5x^2$ is even, odd, or neither.

Accepted Answer

Even

Question 9

Find the average rate of change of $$f(x) = 3x - 9$$ from $$x = 1 to$$ $$x = 3.$$

Accepted Answer

$$3$$

Question 10

A manufacturer’s revenue is given by $$R(p) = -5p^2$ + 1050p. $$What price $$p$$ maximizes revenue, and what is the maximum revenue?

Accepted Answer

$$p = 105, R = 55,125$$

Question 11

Given the function $$f(x) = -x^2$ - 2x - 4$$, does it have a maximum or minimum value, and what is that value?

Accepted Answer

Maximum at $$x = -1$$, value $$-3$$

Question 12

Which of the following best describes the intervals where the function $$f(x) = x^2$ - 10x is $$increasing?

Accepted Answer

$$x \u003e 5$$

Question 13

Given the piecewise function $$f(x) = \begin{cases} x - 5 & x \u003c 1 \ 3 & x \geq 1 \end{cases}$$, what is the range?

Accepted Answer

$$(-\infty, 3]$$

Question 14

A projectile is fired from a cliff. Its height is given by $$h(x) = -\dfrac{32x^2$}{(210)^2$} + x + 500. $$What is the maximum height?

Accepted Answer

$$552.8$$ feet

Question 15

Given the data: $$x = 0, 3, 4, 5, 12$$ and $$y = 8, 2, 6, 9, 12$$, which statement is true about the line of best fit?

Accepted Answer

The line of best fit has a positive slope and fits the data well.

Question 16

Which of the following functions is linear?

Accepted Answer

$$f(x) = 2x + 3$$

Question 17

Given $$f(x) = 3x^2$ - 5x - 5$$, what is the $$y-$$intercept?

Accepted Answer

$$-5$$

Question 18

If $$f(x) is $$even, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$ for all x$

Question 19

Which of the following best describes the transformation from $$f(x) = \dfrac{1}{x} to$$ $$f(x) = \dfrac{3}{x}$$?

Accepted Answer

Vertical stretch by a factor of 3

College Algebra Exam Review: Functions, Graphs, and Rates of Change

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