Q: Which of the following best describes the domain of the function $f(x) = \dfrac{1}{x-4}$?

All real numbers except $x = 4$

Q: Which of the following best describes the end behavior of the function $f(x) = -3x^4 + 2x^2 - 7$?

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

Question 1

Which of the following is the correct solution to the equation $\sqrt{x+5} = 3$?

Accepted Answer

$x = 4$

Question 2

A biologist is studying the growth of a bacterial colony, which can be modeled by the function $N(t) = 200 \cdot 2^t$, where $N$ is the number of bacteria and $t$ is the time in hours. How many bacteria will there be after 3 hours?

Accepted Answer

$1600$

Question 3

Which of the following is the equation of a circle with center at $(2, -3)$ and radius $5$?

Accepted Answer

$(x-2)^2 + (y+3)^2 = 25$

Question 4

Given the function $f(x) = 2x^2 - 4x + 1$, which of the following describes the effect of replacing $x$ with $x-3$ in the function?

Accepted Answer

The graph shifts 3 units to the right.

Question 5

A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 12x - 16$, 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 $20$ thousand dollars at $x = 3$ thousand units.

Question 6

Which of the following is the correct solution set for the inequality $2x - 5 < 7$?

Accepted Answer

$x < 6$

Question 7

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

Accepted Answer

$10$

Question 8

Which of the following best describes the domain of the function $f(x) = \dfrac{1}{x-4}$?

Accepted Answer

All real numbers except $x = 4$

Question 9

A line passes through the points $(1, 2)$ and $(3, 6)$. What is the equation of the line in slope-intercept form?

Accepted Answer

$y = 2x$

Question 10

Which transformation is applied to the graph of $y = f(x)$ to obtain $y = f(-x)$?

Accepted Answer

Reflection across the $y$-axis

Question 11

Given the function $f(x) = |x-2|$, what is the range of $f(x)$?

Accepted Answer

$[0, \infty)$

Question 12

A chemical reaction’s temperature $T$ (in degrees Celsius) over time $t$ (in minutes) is modeled by $T(t) = 5t + 20$. What is the temperature after 8 minutes?

Accepted Answer

$60$ degrees Celsius

Question 13

Which of the following is the correct vertex form of the quadratic $y = x^2 - 6x + 5$?

Accepted Answer

$y = (x-3)^2 - 4$

Question 14

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

Accepted Answer

$x^2 + 2x + 1$

Question 15

A medical researcher models the concentration $C$ of a drug in the bloodstream by $C(t) = 50e^{-0.2t}$, where $t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$18$

Question 16

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

Accepted Answer

$(2, 3)$

Question 17

Which of the following best describes the end behavior of the function $f(x) = -3x^4 + 2x^2 - 7$?

Accepted Answer

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

Question 18

If the line $y = 2x + 1$ is perpendicular to another line, what is the slope of the other line?

Accepted Answer

$-\dfrac{1}{2}$

Question 19

Which of the following is the correct solution to the equation $|3x - 4| = 8$?

Accepted Answer

$x = 4$ or $x = -\dfrac{4}{3}$

Question 20

A quadratic function models the height $h$ (in meters) of a ball thrown upward as $h(t) = -4.9t^2 + 19.6t + 2$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$2$ seconds

College Algebra: Core Concepts and Functions Study Guide

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