Question 1

Simplify the rational expression: $$\frac{x^2$ - 9}{x^2$ + 3x}$$

Accepted Answer

$$\frac{x-3}{x}$$

Question 2

Find the domain of the function $$R(x) = \frac{2x+5}{x+4}.$$

Accepted Answer

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

Question 3

Which of the following is the correct horizontal asymptote for $$R(x) = \frac{x+5}{x^2$ - 4x + 8}$$?

Accepted Answer

$$y = 0$$

Question 4

Given $$R(x) = \frac{3x^2$ - 2x + 1}{x^2$ + 3x}$$, what values must be excluded from the domain?

Accepted Answer

$$x = 0$$ and $$x = -3$$

Question 5

Simplify the expression: $$\frac{2x^2$ + 8x}{4x^2$ + 16x + 16}$$

Accepted Answer

$$\frac{x}{2(x+2)}$$

Question 6

Solve for $$x$$: $$\frac{7}{x+2} = 3$$

Accepted Answer

$$x = -5$$

Question 7

Which of the following is the correct vertical asymptote for $$R(x) = \frac{x+5}{x(x+2)}$$?

Accepted Answer

$$x = 0$$ and $$x = -2$$

Question 8

Given $$R(x) = \frac{5x}{x^2$ - 64}$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$(0, 0)$$

Question 9

Which of the following describes the behavior of the graph of $$R(x) = \frac{5x}{(x-8)(x+8)} at$$ $$x = 8$$?

Accepted Answer

The graph approaches infinity with opposite signs on each side

Question 10

Solve the inequality: $$\frac{x-3}{x+2} \u003e 0$$

Accepted Answer

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

Question 11

Which transformation is applied to the graph of $$f(x) = \frac{1}{x} to $$obtain $$R(x) = \frac{1}{x+3} - 2$$?

Accepted Answer

Shift left 3 units, down 2 units

Question 12

Given $$R(x) = \frac{x^2$ + 4x + 3}{x^2$ - 4x + 3}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 13

If a rational function has a zero in the numerator and a zero in the denominator at the same $$x-$$value, what does the graph have at that $$x-$$value?

Accepted Answer

A hole

Question 14

Which of the following is the correct simplified form of $$\frac{x^2$ - 9}{x^2$ + 3x}$$?

Accepted Answer

$$\frac{x-3}{x}$$

Question 15

Given the function $$R(x) = \frac{1}{x-2}$$, which of the following statements is true?

Accepted Answer

The graph has a vertical asymptote at $$x = 2$$

Question 16

If $$R(x) = \frac{3x+1}{x^2$+4x+3}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 1/3)$$

Question 17

Which of the following best describes the end behavior of $$R(x) = \frac{2x^2$ + 3x + 1}{x^2$ + 4x + 4} as$$ $$x 	o \infty$$?

Accepted Answer

$$y 	o 2$$

Question 18

Given $$R(x) = \frac{5x}{x^2$ - 64}$$, for which $$x-$$values does the function have vertical asymptotes?

Accepted Answer

$$x = 8$$ and $$x = -8$$

Question 19

Which of the following is the correct solution to the equation $$\frac{x}{x-3} - \frac{5x}{x+1} = 0$$?

Accepted Answer

$$x = 0$$

Question 20

A rational function $$R(x)$$ has $$x-$$intercepts at $$x = -4 ($$crosses) and $$x = 9 ($$touches), and vertical asymptotes at $$x = -3 ($$multiplicity 1) and $$x = 4 ($$multiplicity 2). Which of the following is true about the behavior at $$x = 4$$?

Accepted Answer

The graph touches and turns at the asymptote

Rational Expressions and Functions: Precalculus Study Guide

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