Q: Which of the following is the correct graph for $f(x) = -x^2$ compared to $f(x) = x^2$?

It is reflected over the x-axis

Question 1

Which of the following best describes the domain of the function $f(x) = \sqrt{x-3}$?

Accepted Answer

$x \geq 3$

Question 2

Given the function $f(x) = 2x^2 - 5x + 3$, what is the vertex of its graph?

Accepted Answer

$(1.25, 0.875)$

Question 3

Which of the following is the correct composition of the functions $f(x) = x^2$ and $g(x) = x+1$ evaluated at $x=2$ for $f(g(x))$?

Accepted Answer

$9$

Question 4

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 500 \cdot 2^{t/3}$

Question 5

Which of the following is the inverse of the function $f(x) = 3x - 7$?

Accepted Answer

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

Question 6

A quadratic function models the height $h$ (in meters) of a ball thrown upward as $h(t) = -4.9t^2 + 20t + 2$. What is the maximum height reached by the ball?

Accepted Answer

$22.41$ meters

Question 7

Which of the following is the correct solution to the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 1$

Question 8

Which transformation occurs to the graph of $f(x) = x^2$ when it is changed to $f(x) = (x-4)^2 + 5$?

Accepted Answer

Shift right 4 units and up 5 units

Question 9

If $f(x) = \log_{2}(x)$, what is the value of $f(8)$?

Accepted Answer

$3$

Question 10

A car depreciates in value by 15% each year. If the initial value is $V_0$, which equation models the value $V$ after $t$ years?

Accepted Answer

$V = V_0 \cdot (0.85)^t$

Question 11

Which of the following is the correct factorization of $x^2 - 5x + 6$?

Accepted Answer

$(x-2)(x-3)$

Question 12

Given $f(x) = x^3$ and $g(x) = 2x$, what is the sum $f(x) + g(x)$?

Accepted Answer

$x^3 + 2x$

Question 13

Which of the following is the correct solution to the inequality $2x - 5 < 9$?

Accepted Answer

$x < 7$

Question 14

If $f(x) = x^2$ and $g(x) = \sqrt{x}$, what is the domain of the composition $f(g(x))$?

Accepted Answer

$x \geq 0$

Question 15

Which of the following is the correct expanded form of $(x+2)^2$?

Accepted Answer

$x^2 + 4x + 4$

Question 16

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = 5x + 20$, where $x$ is the number of units sold. What is the revenue if 100 units are sold?

Accepted Answer

$520$ thousand dollars

Question 17

Which of the following is the correct solution to the equation $e^{x} = 7$?

Accepted Answer

$x = \ln{7}$

Question 18

Which of the following is the correct graph for $f(x) = -x^2$ compared to $f(x) = x^2$?

Accepted Answer

It is reflected over the x-axis

Question 19

Which of the following is the correct solution to the system of equations using matrices: $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}$?

Accepted Answer

$x = 1, y = 2$

College Algebra Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards