$$\frac{x + 3}{x - 3}$$, for $$x \neq 3$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 2

Given the rational function $$f(x) = \frac{x^2$ - 4}{x^2$ - 1}$$, what are the equations of its vertical asymptotes?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 3

What is the horizontal asymptote of the function $$f(x) = \frac{2x^2$ + 3}{x^2$ - 5}$$?

Accepted Answer

$$y = 2$$

Question 4

Which of the following is the correct domain for the function $$F(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 5

If $$f(x) = |x|$$, which of the following statements is true about its graph?

Accepted Answer

It is symmetric about the $$y-$$axis

Question 6

Consider the piecewise function $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}. $$What is $$f(-2)$$?

Accepted Answer

$$4$$

Question 7

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is f$$[g(3)]$$?

Accepted Answer

$$19$$

Question 8

Which pair of functions are inverses of each other?

Accepted Answer

$$f(x) = 3x + 2$$ and $$g(x) = \frac{x - 2}{3}$$

Question 9

If $$f(x) = e^x$$, which of the following is true about its graph?

Accepted Answer

It has a horizontal asymptote at $$y = 0$$

Question 10

Which of the following is the correct range for the function $$y = a^x$$ where $$a \u003e 1$$?

Accepted Answer

$$(0, \infty)$$

Question 11

If $$a = 0.5$$, which statement best describes the function $$y = a^x$$?

Accepted Answer

It is decreasing for all real $$x$$

Question 12

Solve for $$x$$: $$2^x = 8$$

Accepted Answer

$$x = 3$$

Question 13

Which of the following is the correct logarithmic form of the equation $$x = 5^y$$?

Accepted Answer

$$y = \log_5$(x)$$

Question 14

Convert the logarithmic equation $$y = \ln(x) to $$its equivalent exponential form.

Accepted Answer

$$x = e^y$$

Question 15

A population of bacteria doubles every hour. If the initial population is 100, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 100 \cdot 2^t$$

Question 16

Which of the following statements about the function $$f(x) = \frac{1}{x} is $$true?

Accepted Answer

It has a vertical asymptote at $$x = 0$$

Question 17

If $$f(x) = \sqrt[3]{x}$$, what is the range of $$f$$?

Accepted Answer

All real numbers

Question 18

Which of the following is a correct simplification of $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\frac{x + 3}{x - 3}$$, for $$x 
eq 3$$

Question 19

If $$f(x) = 2^x$$ and $$g(x) = \log_2$(x)$$, what is $$f[g(8)]$$?

Accepted Answer

$$8$$

Algebraic, Exponential, and Introductory Logarithmic Functions: Study Guide

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