Question 1

Based on the table provided, what is $$\lim_{x 	o 0} \frac{1}{x^2$}$$?

Accepted Answer

$$\infty$$

Question 2

Which of the following best describes the behavior of $$y = \frac{1}{x^2$} as$$ $$x$$ approaches $$0$$ from either side?

Accepted Answer

The function approaches $$\infty.$$

Question 3

Given the graph shown, which of the following statements is true about the vertical asymptote?

Accepted Answer

There is a vertical asymptote at $$x = 0.$$

Question 4

For the function $$f(x) = \frac{x-4}{x^2$-9x+20}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 5$$ only

Question 5

What is the horizontal asymptote of $$y = \frac{3x^3$ + 9x^2$ - 2}{x^2$ - x + 1} as$$ $$x 	o \infty$$?

Accepted Answer

There is no horizontal asymptote.

Question 6

Evaluate $$\lim_{x 	o \infty} \frac{x+1}{x^2$+3}.$$

Accepted Answer

$$0$$

Question 7

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

Accepted Answer

$$y = \frac{x^2$+2x+1}{3x^3$-2x^2$$}$

Question 8

Find the oblique (slant) asymptote of $$f(x) = \frac{x^2$-4}{x-1}.$$

Accepted Answer

$$y = x + 1$$

Question 9

If $$\lim_{x 	o a} f(x) = \infty$$, what does this imply about the graph of $$y = f(x)$$?

Accepted Answer

There is a vertical asymptote at $$x = a.$$

Question 10

Evaluate $$\lim_{x 	o -\infty} -x^3$.

Accepted Answer

$$\infty$$

Question 11

Which of the following best describes the horizontal asymptote of $$y = \frac{x^2$-1}{x^2$+3x+2}$$?

Accepted Answer

$$y = 1$$

Question 12

For the function $$y = \frac{x^2$-4x+5}{x-2}$$, what type of asymptote does it have?

Accepted Answer

Vertical asymptote at $$x = 2$$ and oblique asymptote

Question 13

Which of the following limits is an example of an infinite limit at infinity?

Accepted Answer

$$\lim_{x 	o \infty} e^x$$

Question 14

A rational function has a numerator of degree 2 and a denominator of degree 3. What is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 15

Given $$f(x) = \frac{x-4}{(x-4)(x-5)}$$, what is $$\lim_{x 	o 4} f(x)$$?

Accepted Answer

$$-1$$

Question 16

Which of the following is true about the function $$y = \frac{1}{x} as$$ $$x 	o \infty$$?

Accepted Answer

The function approaches $$0.$$

Question 17

If the degree of the numerator is exactly one more than the degree of the denominator in a rational function, what type of asymptote exists?

Accepted Answer

Oblique (slant) asymptote

Question 18

Evaluate $$\lim_{x 	o -\infty} \frac{\pi^3$}{3x^2$}.$$

Accepted Answer

$$0$$

Question 19

Which of the following is the correct process to find vertical asymptotes of a rational function?

Accepted Answer

Factor numerator and denominator, reduce, then set denominator equal to zero and solve.

2.6

Study Guide - Practice Questions