Question 1

Let $f(x) = -7x + 3$ and $g(x) = 2x + 5$. What is $(f \circ g)(-2)$?

Accepted Answer

$-25$

Question 2

Kasper deposits $5,500 into an account that pays 2.5% interest, compounded quarterly. If he makes no changes to the account, which formula gives the amount in the account after 8 years?

Accepted Answer

$A = 5500(1 + \frac{0.025}{4})^{32}$

Question 3

Let $f(x) = \frac{1}{x}(2x - 5)$. What is the domain of $f$?

Accepted Answer

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

Question 4

Use properties of logarithms to solve $125^{3x+4} = 25$. What is the value of $x$?

Accepted Answer

$x = -\frac{7}{3}$

Question 5

Let $f(x) = \sqrt{x + 7}$. What is $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = x^2 - 7$

Question 6

A company orders custom water bottles as thank-you gifts. There is a one-time processing fee of $40.00 and an additional cost of $6.50 per bottle. Which function models the total cost $C(x)$ for $x$ bottles?

Accepted Answer

$C(x) = 40 + 6.50x$

Question 7

Given the graph of $g(x)$ as a transformation of $f(x) = |x|$, which of the following describes a reflection over the $x$-axis and a vertical shift down by 3 units?

Accepted Answer

$g(x) = -|x| - 3$

Question 8

Use properties of logarithms to evaluate $\log_{10} 10,000$.

Accepted Answer

$4$

Question 9

Let $f(x) = 2(x + 1)^3$ and $g(x) = x^2$. What is $(g \circ f)(-3)$?

Accepted Answer

$512$

Question 10

Rewrite $\ln[e^{x + 3}]$ as a sum or difference of logarithms.

Accepted Answer

$x + 3$

Question 11

A city had a population of 48,900 in 2018, increasing at a rate of 2.7% per year. Which equation models the population $A(t)$ after $t$ years?

Accepted Answer

$A(t) = 48,900(1.027)^t$

Question 12

Rewrite $\log_b a = 17$ in exponential form.

Accepted Answer

$b^{17} = a$

Question 13

If $f(x) = \sqrt{x + 7}$, what is the domain of $f$?

Accepted Answer

$[-7, \infty)$

Question 14

Which of the following is the correct average cost function $\overline{C}(x)$ for $x$ water bottles, given $C(x) = 40 + 6.50x$?

Accepted Answer

$\overline{C}(x) = \frac{40 + 6.50x}{x}$

Question 15

Use properties of logarithms to evaluate $\ln \frac{1}{e^2}$.

Accepted Answer

$-2$

Question 16

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

Accepted Answer

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

Question 17

A company orders 150 water bottles. The total cost is $C(150) = 40 + 6.50 	imes 150$. What is the average cost per bottle?

Accepted Answer

$\$6.77$

Question 18

Which transformation maps $f(x) = |x|$ to $g(x) = -|x| - 3$?

Accepted Answer

Reflection over $x$-axis and vertical shift down 3 units

Question 19

If $A(t) = 48,900(1.027)^t$, what is the predicted population in 2026?

Accepted Answer

$59,800$

College Algebra: Functions, Exponents, and Logarithms – Exam Study Guide

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