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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