Q: If $$f(x) = \frac{1}{x-2}$$, which of the following statements is true?

As $$x \to 2^+$$, $$f(x) \to +\infty$$

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 the function $$f(x) = \frac{1}{x}$$, 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 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 $$f(x) = \frac{1}{x+1}$$, what is $$\lim\limits_{x 	o -1^+} f(x)$$?

Accepted Answer

$$+\infty$$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

$$f(x) 	o 0$$

Question 9

For the function $$f(x) = \frac{1}{(x-2)^2$}$$, what happens to $$f(x) as$$ $$x$$ approaches $$2$$?

Accepted Answer

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

Question 10

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

Accepted Answer

$$y = 2$$

Question 11

Suppose $$f(x) = \frac{1}{x-3} + 2. $$What is $$\lim\limits_{x 	o 3^-} f(x)$$?

Accepted Answer

$$-\infty$$

Question 12

Which of the following functions has a vertical asymptote at $$x = -4$$ and a horizontal asymptote at $$y = -2$$?

Accepted Answer

$$f(x) = \frac{1}{x+4} - 2$$

Question 13

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

Accepted Answer

As $$x 	o 2^+$$, $$f(x) 	o +\infty$$

Question 14

Given $$f(x) = \frac{1}{x-1}$$, what is the value of $$\lim\limits_{x 	o 1} f(x)$$?

Accepted Answer

The limit does not exist

Question 15

Which of the following best describes the domain of $$f(x) = \frac{1}{x-2} + 3$$?

Accepted Answer

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

Question 16

For the function $$f(x) = \frac{1}{x-2}$$, what is the value of $$\lim\limits_{x 	o 2^-} f(x)$$?

Accepted Answer

$$-\infty$$

Question 17

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

Accepted Answer

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

Question 18

A rational function has a vertical asymptote at $$x = 5$$ and a horizontal asymptote at $$y = -1. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \frac{1}{x-5} - 1$$

Question 19

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

Accepted Answer

$$(0, \infty)$$

Question 20

Suppose $$f(x) = \frac{1}{x-2} + 3. $$What is $$\lim\limits_{x 	o \infty} f(x)$$?

Accepted Answer

$$3$$

E2,E3

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