Question 1

Given the points $A(2, -3)$ and $B(-4, 5)$, what is the distance between $A$ and $B$?

Accepted Answer

$\sqrt{52}$

Question 2

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

Accepted Answer

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

Question 3

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 200 \cdot 3^{t/4}$

Question 4

Which of the following functions is even?

Accepted Answer

$f(x) = x^2 + 1$

Question 5

Solve the inequality $2x - 5 > 7$.

Accepted Answer

$x > 6$

Question 6

What is the domain of the function $f(x) = \sqrt{5 - x}$?

Accepted Answer

$(-\infty, 5]$

Question 7

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

Accepted Answer

$9$

Question 8

Which of the following is the $y$-intercept of the function $f(x) = 2x^2 - 3x + 5$?

Accepted Answer

$(0, 5)$

Question 9

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = 50x - x^2$, where $x$ is the number of units sold (in thousands). What is the maximum revenue?

Accepted Answer

$625$ thousand dollars

Question 10

Which transformation maps the graph of $y = f(x)$ to $y = f(x - 4) + 2$?

Accepted Answer

Right 4 units, up 2 units

Question 11

Solve the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$

Accepted Answer

$x = 2,\ y = 3$

Question 12

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

Accepted Answer

$x = 32$

Question 13

Find the midpoint of the segment joining $(-6, 2)$ and $(4, -8)$.

Accepted Answer

$( -1, -3 )$

Question 14

Which of the following is the range of the function $f(x) = 2^x$?

Accepted Answer

$(0, \infty)$

Question 15

If $f(x) = \ln(x)$, what is the domain of $f$?

Accepted Answer

$(0, \infty)$

Question 16

Which of the following is the $x$-intercept of the function $f(x) = x^2 - 9$?

Accepted Answer

$(-3, 0)$ and $(3, 0)$

Question 17

Solve the quadratic equation $x^2 - 6x + 5 = 0$.

Accepted Answer

$x = 1$ and $x = 5$

Question 18

Which of the following is the correct simplification of $\log_{10}(1000)$?

Accepted Answer

$3$

Question 19

A medication decays in the bloodstream according to $C(t) = 50e^{-0.2t}$, where $C$ is the concentration in mg/L and $t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$18.4$ mg/L

Comprehensive Study Guide: College Algebra Final Exam Topics (Units 1-3)

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