Question 1

Which of the following best describes the graph of the function $f(x) = \sqrt{x}$?

Accepted Answer

A curve that starts at $(0,0)$ and increases slowly, only defined for $x \geq 0$

Question 2

Given the set $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$, what is $A \cap B$?

Accepted Answer

$\{2, 3\}$

Question 3

If $f(x) = 2x + 1$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$f(g(2)) = 2 \cdot 4 + 1 = 9$

Question 4

Which of the following is the solution set for $|x - 3| = 5$?

Accepted Answer

$x = 8$ or $x = -2$

Question 5

Given the function $f(x) = x^2 - 4x + 3$, what are the zeros of the function?

Accepted Answer

$x = 1$ and $x = 3$

Question 6

Which of the following represents the sum $\sum_{i=1}^{4} i^2$?

Accepted Answer

$1^2 + 2^2 + 3^2 + 4^2 = 30$

Question 7

If $A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 0 \ 1 & 2 \end{pmatrix}$, what is the $(1,2)$ entry of $A + B$?

Accepted Answer

$4$

Question 8

Which of the following is the domain of the function $f(x) = \frac{1}{x-2}$?

Accepted Answer

$x 
eq 2$

Question 9

A real-world application: A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $18$ at $x = 2$

Question 10

Which of the following is the solution to the system of equations: $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$(x, y) = (3, 2)$

Question 11

Which of the following is the correct simplification of $\sqrt{50}$?

Accepted Answer

$5\sqrt{2}$

Question 12

Given the scatter plot of a set of data points that form a roughly upward trend, which type of correlation is most likely present?

Accepted Answer

Positive correlation

Question 13

If $f(x) = x^2$ and $g(x) = x + 1$, what is $f(g(2))$?

Accepted Answer

$f(3) = 9$

Question 14

Which of the following is the range of the function $f(x) = x^2$ for $x \in \mathbb{R}$?

Accepted Answer

$[0, \infty)$

Question 15

If $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, what is $A \cup B$?

Accepted Answer

$\{1, 2, 3, 4, 5, 6\}$

Question 16

Which of the following is the solution to $2x^2 - 8 = 0$?

Accepted Answer

$x = 2$ or $x = -2$

Question 17

If $f(x) = 3x - 7$, what is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \frac{x + 7}{3}$

Question 18

Which of the following is the determinant of the matrix $\begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}$?

Accepted Answer

$2 	imes 4 - 3 	imes 1 = 5$

Question 19

A quadratic function models the height $h$ (in meters) of a ball thrown upward as $h(t) = -5t^2 + 20t + 2$. What is the maximum height reached by the ball?

Accepted Answer

$22$ meters at $t = 2$ seconds

Key Concepts in College Algebra: Functions, Graphs, Matrices, and Series

Study Guide - Practice Questions

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