Question 1

Which transformation is applied to the parent function $$f(x) = \frac{1}{x} to $$obtain $$g(x) = \frac{1}{x-2} + 3$$?

Accepted Answer

Shift right by 2 units and up by 3 units

Question 2

Given $$g(x) = \frac{1}{x+3} - 2$$, what are the equations of the vertical and horizontal asymptotes?

Accepted Answer

Vertical: $$x = -3$$, Horizontal: $$y = -2$$

Question 3

For the rational function $$f(x) = \frac{2x-3}{x-1}$$, what is the domain?

Accepted Answer

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

Question 4

What is the $$y-$$intercept of $$f(x) = \frac{2x-3}{x-1}$$?

Accepted Answer

$$(0, 3)$$

Question 5

A rational function $$f(x)$$ has a hole at $$x = 2. $$Which of the following must be true?

Accepted Answer

Both the numerator and denominator have a factor of $$(x-2)$$

Question 6

Given $$f(x) = \frac{x^2$+3}{x^2$+5x+6}$$, what are the vertical asymptotes?

Accepted Answer

$$x = -2$$ and $$x = -3$$

Question 7

For $$f(x) = \frac{2x^2$}{x^2$-4}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 8

Which of the following describes the end behavior of $$f(x) = \frac{2x^2$}{x^2$-4} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 2$$

Question 9

If $$f(x) = \frac{x^2$-9}{x^2$-4}$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 10

For $$f(x) = \frac{x^2$+3}{x^2$+5x+6}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 0.5)$$

Question 11

Which transformation is applied to $$f(x) = \frac{1}{x} to $$obtain $$g(x) = -\frac{1}{x+1} + 2$$?

Accepted Answer

Reflect over $$x-$$axis, shift left by 1, up by 2

Question 12

A rational function $$f(x)$$ has a vertical asymptote at $$x = 4$$ and a horizontal asymptote at $$y = 0. $$Which could be its equation?

Accepted Answer

$$f(x) = \frac{2x}{x-4}$$

Question 13

For $$f(x) = \frac{2x-3}{x-1}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 1$$

Question 14

If $$f(x) = \frac{x^2$+3}{x^2$+5x+6}$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$ except $$y = 0$$

Question 15

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

Accepted Answer

It has vertical asymptote at $$x = 0$$ and horizontal asymptote at $$y = 0$$

Question 16

For $$f(x) = \frac{2x^2$}{x^2$-4}$$, what are the vertical asymptotes?

Accepted Answer

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

Question 17

If $$f(x) = \frac{x^2$-9}{x^2$-4}$$, what is the domain?

Accepted Answer

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

Question 18

Which of the following rational functions has a hole at $$x = 1$$?

Accepted Answer

$$f(x) = \frac{(x-1)(x+2)}{(x-1)(x-3)}$$

Graphing Rational Functions and Transformations: Study Notes for College Algebra

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