Question 1

Which of the following is the correct equation for a rational function with a vertical asymptote at $$x = -2$$ and a horizontal asymptote at $$y = 3$$?

Accepted Answer

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

Question 2

Given $$f(x) = \frac{1}{x}$$, what happens to $$f(x) as$$ $$x$$ approaches $$0$$ from the positive side?

Accepted Answer

$$f(x)$$ approaches $$+\infty$$

Question 3

What is the domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

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

Question 4

Which of the following best describes the transformation from $$f(x) = \frac{1}{x} to$$ $$g(x) = \frac{1}{x-2} + 1$$?

Accepted Answer

Shift right 2 units and up 1 unit

Question 5

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

Accepted Answer

$$x = 3$$

Question 6

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

Accepted Answer

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

Question 7

Evaluate $$\displaystyle \lim_{x 	o 2} \frac{x^2$ - 4}{x - 2}.$$

Accepted Answer

$$4$$

Question 8

Which of the following statements is true about the function $$f(x) = \frac{1}{(x-2)^2$} as$$ $$x$$ approaches $$2$$?

Accepted Answer

$$f(x)$$ approaches $$+\infty$$ from both sides

Question 9

If $$f(x) = \frac{x-2}{x-2}$$, what is $$\displaystyle \lim_{x 	o 2} f(x)$$?

Accepted Answer

$$1$$

Question 10

A rational function has a horizontal asymptote at $$y = -2$$ and a vertical asymptote at $$x = 1. $$Which of the following could be its equation?

Accepted Answer

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

Question 11

Given the graph of $$f(x) = \frac{1}{x}$$, which of the following describes its end behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 12

For $$f(x) = \frac{1}{x-2}$$, what is $$\displaystyle \lim_{x 	o 2^-} f(x)$$?

Accepted Answer

$$-\infty$$

Question 13

Which of the following best describes the domain of $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

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

Question 14

Suppose $$f(x) = \frac{1}{x-1} + 2. $$What is the equation of the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 15

Evaluate $$\displaystyle \lim_{x 	o 0^+} \frac{1}{x}.$$

Accepted Answer

$$+\infty$$

Question 16

Which of the following is true about the function $$f(x) = \frac{1}{x-2} + 3$$?

Accepted Answer

It has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 3$$

Question 17

If $$f(x) = \frac{1}{x-2}$$, what is $$\displaystyle \lim_{x 	o 2^+} f(x)$$?

Accepted Answer

$$+\infty$$

Question 18

Given $$f(x) = \frac{1}{x-2}$$, which of the following best describes the behavior of $$f(x) as$$ $$x$$ approaches $$2$$ from the left?

Accepted Answer

$$f(x)$$ decreases without bound

Question 19

Which of the following is the correct arrow notation for $$f(x) = \frac{1}{x} as$$ $$x 	o 0^-$$?

Accepted Answer

$$f(x) 	o -\infty$$

E2-E3

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