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

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 $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$, 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

$$x \u003e 1$$

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

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