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 $$f(x) = \frac{1}{x}$$, what is the equation for the function reflected over the y-axis and shifted down by 4 units?

Accepted Answer

$$f(x) = \frac{1}{-x} - 4$$

Question 3

What is the vertical asymptote of $$f(x) = \frac{2x+1}{x-3}$$?

Accepted Answer

$$x = 3$$

Question 4

For the rational function $$f(x) = \frac{x^2$-4}{x-2}$$, what is the behavior at $$x=2$$?

Accepted Answer

Removable discontinuity (hole) at $$x=2$$

Question 5

What is the horizontal asymptote of $$f(x) = \frac{3x^2$+1}{2x^2$-5}$$?

Accepted Answer

$$y = \frac{3}{2}$$

Question 6

If $$f(x) = \frac{1}{x}$$, which transformation results in $$f(x) = -\frac{1}{x+1}$$?

Accepted Answer

Reflect over the x-axis and shift left by 1 unit

Question 7

A rational function $$f(x) = \frac{x+2}{x-1} is $$transformed to $$g(x) = \frac{x+2}{x-1} + 4. $$What is the effect of this transformation?

Accepted Answer

Vertical shift up by 4 units

Question 8

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

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 9

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

Accepted Answer

$$y = 1$$

Question 10

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

Accepted Answer

$$f(x) 	o 2$$

Question 11

A medical dosage model is given by $$D(x) = \frac{10}{x-2}$$, where $$x is $$the number of hours after administration. What is the minimum value of $$x$$ for which the dosage is defined?

Accepted Answer

$$x \u003e 2$$

Question 12

For $$f(x) = \frac{x+1}{x^2$-4}$$, which value of $$x$$ creates a vertical asymptote?

Accepted Answer

$$x = 2$$

Question 13

If $$f(x) = \frac{1}{x}$$, what is the effect of the transformation $$f(x) = \frac{1}{x+3} - 2$$?

Accepted Answer

Shift left by 3 units and down by 2 units

Question 14

A rational function $$f(x) = \frac{x^2$-9}{x-3}$$ has a hole at $$x=3. $$What is the y-value of the hole?

Accepted Answer

$$y = 6$$

Question 15

Which of the following rational functions has a horizontal asymptote at $$y=0$$?

Accepted Answer

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

Question 16

For $$f(x) = \frac{1}{x-1}$$, what is the range of the function?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 17

A rational function $$f(x) = \frac{x^2$-4}{x^2$-1} is $$used to model a chemical reaction rate. What are the vertical asymptotes?

Accepted Answer

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

Question 18

Given $$f(x) = \frac{1}{x}$$, which transformation results in $$f(x) = \frac{1}{2x-4}$$?

Accepted Answer

Horizontal compression by $$\frac{1}{2}$$ and shift right by 2 units

Question 19

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

Accepted Answer

$$x = -2$$

Graphing Rational Functions: Transformations and Asymptotes

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