Q: Which of the following is the correct graph for the function $f(x) = -x^2 + 4x - 3$?

A parabola opening downwards with vertex at $(2, 1)$

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

$(-\infty, 0) \cup (0, \infty)$

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

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 3

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

Accepted Answer

$2 < x < 3$

Question 4

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

Accepted Answer

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

Question 5

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height $h$ after $t$ seconds is given by $h(t) = -4.9t^2 + 10t + 2$. What is the maximum height reached by the ball?

Accepted Answer

$12.2$ meters

Question 6

Which of the following is the correct graph for the function $f(x) = -x^2 + 4x - 3$?

Accepted Answer

A parabola opening downwards with vertex at $(2, 1)$

Question 7

If $f(x) = 2x^2 - 5x + 1$ and $g(x) = x - 3$, what is $(f \circ g)(x)$?

Accepted Answer

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

Question 8

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

Accepted Answer

$x = 32$

Question 9

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

Accepted Answer

$V = V_0 \cdot 0.85^t$

Question 10

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 11

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

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 12

Which of the following is the correct solution for $e^{2x} = 7$?

Accepted Answer

$x = \frac{1}{2}\ln(7)$

Question 13

Which of the following is the correct vertex of the quadratic function $f(x) = x^2 - 6x + 8$?

Accepted Answer

$(3, -1)$

Question 14

Which of the following is the correct solution to $|2x - 5| = 7$?

Accepted Answer

$x = 6$ or $x = -1$

Question 15

Which of the following is the correct solution for the exponential equation $3^{x+1} = 27$?

Accepted Answer

$x = 2$

Question 16

Which of the following is the correct equation for a line passing through $(2, 5)$ with a slope of $-3$?

Accepted Answer

$y = -3x + 11$

Question 17

Which of the following is the correct solution to the inequality $\frac{x+2}{x-1} > 0$?

Accepted Answer

$x < -2$ or $x > 1$

Question 18

Which of the following is the correct solution for $\log_{10}(x^2) = 4$?

Accepted Answer

$x = 100$ or $x = -100$

Question 19

Which of the following is the correct solution for the system $\begin{cases} x + y = 8 \ x - y = 2 \end{cases}$?

Accepted Answer

$(x, y) = (5, 3)$

College Algebra (MAC 1105) Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards