Q: Which of the following describes the end behavior of the polynomial $f(x) = -2x^5 + 3x^2 - 7$?

As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to \infty$

Q: Which of the following is the correct graph transformation for $f(x) = x^2$ to $g(x) = (x - 5)^2 + 3$?

Shift right 5 units and up 3 units

Q: A medication’s concentration in the bloodstream decreases according to $C(t) = 100e^{-0.2t}$, where $t$ is in hours. What is the concentration after 5 hours?

$C(5) = 100e^{-1} \approx 36.79$

Question 1

Which of the following best describes the domain of the function $f(x) = \dfrac{1}{x-3}$?

Accepted Answer

All real numbers except $x = 3$

Question 2

A company’s profit $P$ (in thousands of dollars) is modeled by the quadratic function $P(x) = -2x^2 + 40x - 100$, 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 $300$ at $x = 10$

Question 3

Which of the following is the correct composition of the functions $f(x) = 2x + 1$ and $g(x) = x^2$ evaluated at $x = 3$ for $(f \circ g)(x)$?

Accepted Answer

$(f \circ g)(3) = 2 \cdot 9 + 1 = 19$

Question 4

Given the function $f(x) = |x - 4|$, which statement best describes its graph?

Accepted Answer

It is a V-shaped graph with vertex at $(4, 0)$

Question 5

Which of the following is the solution set for the inequality $x^2 - 5x + 6 < 0$?

Accepted Answer

$2 < x < 3$

Question 6

A population of bacteria grows according to the exponential function $P(t) = 500 \cdot 2^t$, where $t$ is the number of hours. What is the population after 4 hours?

Accepted Answer

$P(4) = 500 \cdot 2^4 = 8000$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

$h_{max} = 22.41$ meters

Question 9

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

Accepted Answer

$(x, y) = (3, 1)$

Question 10

Which of the following describes the end behavior of the polynomial $f(x) = -2x^5 + 3x^2 - 7$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o -\infty$; as $x 	o -\infty$, $f(x) 	o \infty$

Question 11

Which of the following is the correct graph transformation for $f(x) = x^2$ to $g(x) = (x - 5)^2 + 3$?

Accepted Answer

Shift right 5 units and up 3 units

Question 12

Which of the following is the correct solution to the equation $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 13

A medication’s concentration in the bloodstream decreases according to $C(t) = 100e^{-0.2t}$, where $t$ is in hours. What is the concentration after 5 hours?

Accepted Answer

$C(5) = 100e^{-1} \approx 36.79$

Question 14

Which of the following is the correct solution to the rational equation $\dfrac{x}{x-2} = 3$?

Accepted Answer

$x = 6$

Question 15

Which of the following is the correct interval notation for the solution to $|2x - 5| \leq 7$?

Question 16

Which of the following is the correct solution to the equation $2^{x+1} = 16$?

Accepted Answer

$x = 3$

Question 17

Which of the following is the correct solution to the polynomial equation $x^3 - 4x = 0$?

Question 18

Which of the following is the correct solution to the system of equations: $\begin{cases} x + y + z = 6 \ x - y + z = 2 \ 2x + y - z = 5 \end{cases}$?

Accepted Answer

$(x, y, z) = (2, 1, 3)$

College Algebra (Precalculus) Syllabus and Course Overview

Study Guide - Practice Questions

Study Guide - Flashcards