Question 1

What is the domain of the function $$f(x) = \frac{1}{x+4}$$?

Accepted Answer

$$(-\infty, -4) \cup (-4, \infty)$$

Question 2

Given $$f(x) = 4x - 3$$ and $$g(x) = 6x - 6$$, what is $$(f - g)(x)$$?

Accepted Answer

$$-2x + 3$$

Question 3

Find the inverse of the function $$f(x) = -6x - 8.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 8}{-6}$$

Question 4

Write the equation $$\log_4$ x = 3 in $$its equivalent exponential form.

Accepted Answer

$$4^3 = x$

Question 5

A city had 3,483,000 residents in 1994 and is growing at 0.7% annually. Using $$y = 3,483,000 	imes (2.7$$)^{0.007t}$$, estimate the population in 2000 (to the nearest ten-thousand).

Accepted Answer

3,630,000

Question 6

Evaluate $$\ln e^9$ without using a calculator.

Accepted Answer

9

Question 7

Find the accumulated value of an investment of $$8,000 at 9% compounded continuously for 3 years. Use A$$ = $$Pe^{rt}$.

Accepted Answer

$$10,479.72$$

Question 8

Given $$f(x) = 2x - 5$$ and $$g(x) = 8x + 6$$, what is $$(fg)(x)$$?

Accepted Answer

$$16x^2 - 28x - 30$

Question 9

Evaluate $$\log_{10} 100$$ without using a calculator.

Accepted Answer

2

Question 10

Find the domain of the logarithmic function $$f(x) = \ln(5 - x).$$

Accepted Answer

$$(-\infty, 5)$$

Question 11

Write the equation $$\log_3$ 9 = 2 in $$its equivalent exponential form.

Accepted Answer

$$3^2 = 9$

Question 12

Find the domain of the logarithmic function $$f(x) = \log_5$(x + 8).$$

Accepted Answer

$$(-8, \infty)$$

Question 13

Evaluate $$\log_3$ 3$$ without using a calculator.

Accepted Answer

1

Question 14

Evaluate $$\log_2$ \frac{1}{8}$$ without using a calculator.

Accepted Answer

-3

Question 15

Write the equation $$\log_2$ 16 = x in $$its equivalent exponential form.

Accepted Answer

$$2^x = 16$$

Question 16

Find the inverse of the function $$f(x) = 4x - 1.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 1}{4}$$

Question 17

Evaluate $$\ln \frac{1}{e^8$}$$ without using a calculator.

Accepted Answer

-8

Question 18

Given $$f(x) = 9x^2$ - 7x$$ and $$g(x) = 19x - 2$$, find $$(f \circ g)(4).$$

Accepted Answer

48,766

Question 19

Write the equation $$123 = y in $$its equivalent logarithmic form.

Accepted Answer

$$\log_{12} y = 3$$

Question 20

Find the accumulated value of an investment of $$10,000 at 5% compounded semiannually for 9 years. Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$.

Accepted Answer

$$15,596.59$$

College Algebra Unit 4 Review: Functions, Logarithms, and Exponentials

Study Guide - Practice Questions

Study Guide - Flashcards