Q: Given $f(x) = \frac{2x}{x^2 - 2}$ and $g(x) = \frac{2x + 3}{x}$, are $f$ and $g$ inverses of each other?

No, because $f(g(x)) \neq x$ for all $x$ in the domain.

Q: A real-world scenario: A company models its profit $P(x)$ in thousands of dollars as $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units (in hundreds) produced. What is the maximum profit, and for how many units produced does it occur?

Maximum profit is $18$ thousand dollars at $x = 2$ hundred units.

Question 1

Given the function $f(x) = x^2 - 2x - 7$, what is the value of $f(3)$?

Accepted Answer

$-4$

Question 2

Which of the following sets of points represents the graph of a function?

Accepted Answer

$\{(-1, 4), (2, -1), (6, -5), (8, 3), (10, 3)\}$

Question 3

How can the graph of $f(x) = -\sqrt{x - 4}$ be obtained from the graph of $y = \sqrt{x}$?

Accepted Answer

Shift 4 units to the right and reflect across the $x$-axis.

Question 4

Given $f(x) = 2x^2 + 7$, $g(x) = x - 4$, find $(f - g)(3)$.

Accepted Answer

$12$

Question 5

Which of the following equations represents a circle with center $(-8, 6)$ and radius $3$?

Accepted Answer

$(x + 8)^2 + (y - 6)^2 = 9$

Question 6

Determine algebraically whether the function $f(x) = x^2 + x^3$ is even, odd, or neither.

Accepted Answer

Neither

Question 7

Find the distance between the points $(7, 7)$ and $(-6, -7)$.

Accepted Answer

$\sqrt{365}$

Question 8

Which of the following best describes the symmetry of the graph of $y = x^2 - 4$?

Accepted Answer

Symmetric with respect to the $y$-axis only

Question 9

Given $f(x) = 16 - x^2$, $g(x) = 4 - x$, find $(f \div g)(4)$.

Accepted Answer

$-4$

Question 10

Which of the following lines is perpendicular to the line $4x + y = 3$ and passes through the point $(2, 4)$?

Accepted Answer

$y = -\frac{1}{4}x + \frac{9}{2}$

Question 11

Given the piecewise function $f(x) = \begin{cases} 6 & 	ext{if } x \leq -1 \ 4 - 3x & 	ext{if } 0 < x < 3 \ x & 	ext{if } x \geq 3 \end{cases}$, what is $f(2)$?

Accepted Answer

$-2$

Question 12

Which of the following statements about the function $f(x) = x^3 + 13x$ is true?

Accepted Answer

The function is odd.

Question 13

Given $f(x) = \frac{2x}{x^2 - 2}$ and $g(x) = \frac{2x + 3}{x}$, are $f$ and $g$ inverses of each other?

Accepted Answer

No, because $f(g(x)) 
eq x$ for all $x$ in the domain.

Question 14

A circle has the equation $(x - 8)^2 + (y - 6)^2 = 9$. What is the center and radius of the circle?

Accepted Answer

Center $(8, 6)$, radius $3$

Question 15

Which of the following equations is the slope-intercept form of the line passing through $(9, 5)$ and $(0, -3)$?

Accepted Answer

$y = \frac{8}{9}x - 3$

Question 16

Given $f(x) = 5x^2 + 5$, what is $f(-2)$?

Accepted Answer

$25$

Question 17

Which of the following best describes the function $f(x) = x^4 + 2x + 8$?

Accepted Answer

Neither even nor odd

Question 18

A real-world scenario: A company models its profit $P(x)$ in thousands of dollars as $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units (in hundreds) produced. What is the maximum profit, and for how many units produced does it occur?

Accepted Answer

Maximum profit is $18$ thousand dollars at $x = 2$ hundred units.

Question 19

Which of the following is the correct equation of the line passing through $(5, 2)$ and parallel to the line $2x + y = 4$?

Accepted Answer

$y = -2x + 12$

Question 20

Suppose $f(x) = x^2 - 2x - 7$ models the height (in meters) of a projectile at time $x$ seconds. At what time does the projectile reach its minimum height?

Accepted Answer

$x = 1$

College Algebra: Functions, Graphs, and Equations Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards