$\{x \mid x \neq \frac{1}{3}\}$

The function is undefined at $x = 2$ and $x = -2$

$(-\infty, -1) \cup (-1, 2) \cup (2, \infty)$

Question 1

Given the function $f(x) = \frac{5x}{3x-1}$, which of the following is the correct domain of $f(x)$?

Accepted Answer

$\{x \mid x 
eq \frac{1}{3}\}$

Question 2

For the function $f(x) = \frac{x^2-4}{x^2-1}$, which values must be excluded from the domain?

Accepted Answer

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

Question 3

Which of the following interval notations correctly represents all real numbers except $x = 2$?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 4

Given $f(x) = \frac{1}{x^2-9}$, what is the domain of $f(x)$?

Accepted Answer

$x 
eq 3$ and $x 
eq -3$

Question 5

If $f(x) = \sqrt{x-2}$, which of the following is the correct domain?

Accepted Answer

$x \geq 2$

Question 6

Which of the following is the correct formula for the slope of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Question 7

Given the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \ x^2 & x \geq 0 \end{cases}$, what is $f(-3)$?

Accepted Answer

$-1$

Question 8

For the rational function $f(x) = \frac{x^2+1}{x^2-4}$, which of the following statements is true?

Accepted Answer

The function is undefined at $x = 2$ and $x = -2$

Question 9

Which of the following is the correct point-slope form of the equation of a line with slope $m$ passing through $(x_1, y_1)$?

Accepted Answer

$y - y_1 = m(x - x_1)$

Question 10

If $f(x) = \frac{2x+5}{x-3}$, what is the value of $f(4)$?

Accepted Answer

$\frac{13}{1}$

Question 11

Which of the following is NOT a restriction when solving for the domain of a rational function?

Accepted Answer

Numerator must be positive

Question 12

Given $f(x) = \frac{1}{x}$, which of the following is the correct domain?

Accepted Answer

$x 
eq 0$

Question 13

For the function $f(x) = \sqrt{9-x^2}$, which of the following is the correct domain?

Accepted Answer

$-3 \leq x \leq 3$

Question 14

Which of the following is the correct interval notation for all real numbers except $x = -1$ and $x = 2$?

Accepted Answer

$(-\infty, -1) \cup (-1, 2) \cup (2, \infty)$

Question 15

If $f(x) = \frac{x+1}{x^2-1}$, what is the domain of $f(x)$?

Accepted Answer

$x 
eq 1$ and $x 
eq -1$

Question 16

Given $f(x) = \frac{1}{x^2}$, which of the following is the correct domain?

Accepted Answer

$x 
eq 0$

Question 17

For the function $f(x) = \frac{1}{\sqrt{x-1}}$, which of the following is the correct domain?

Accepted Answer

$x > 1$

Question 18

Which of the following is the correct way to write the interval $[a, b]$ in set notation?

Accepted Answer

$\{x \mid a \leq x \leq b\}$

Question 19

If $f(x) = \frac{1}{x-2}$, what is the value of $f(5)$?

Accepted Answer

$\frac{1}{3}$

Business Calculus: Functions, Domains, Interval Notation, and Piecewise Functions

Study Guide - Practice Questions