Q: Let $$f(x) = \frac{2x^3$ + 5x^2$ - 1}{x^2$ - 4}. $$What is the end behavior of $$f(x) as$$ $$x \to \infty$$?

$$f(x) \sim 2x as$$ $$x \to \infty$$

Question 1

Let $$f(x) = \frac{2x^3$ + 5x^2$ - 1}{x^2$ - 4}. $$What is the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) \sim 2x as$$ $$x 	o \infty$$

Question 2

Suppose $$f(x) = \frac{p(x)}{q(x)}$$ where $$p(x)$$ and $$q(x)$$ are polynomials. If $$\deg(p) \u003c \deg(q)$$, what is the horizontal asymptote of $$f(x)$$?

Accepted Answer

$$y = 0$$

Question 3

Given $$f(x) = \frac{3x^2$ + 2x + 1}{x^2$ - 1}$$, which of the following statements is true about its horizontal asymptote?

Accepted Answer

$$y = 3$$

Question 4

For the rational function $$f(x) = \frac{x^2$ + 1}{x^3$ - x}$$, what is the end behavior as $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 5

If $$f(x) = \frac{2x^4$ + 3x^2$}{x^4$ - 5}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 6

Consider $$f(x) = \frac{x^2$ + 1}{x - 2}. $$What is the behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) \sim x$$

Question 7

Suppose $$f(x) = \frac{5x^3$ + 2}{2x^3$ - 7}. $$What is the horizontal asymptote?

Accepted Answer

$$y = \frac{5}{2}$$

Question 8

Let $$f(x) = \frac{2x^2$ + 3x + 1}{x^3$ + 1}. As$$ $$x 	o \infty$$, what does $$f(x)$$ approach?

Accepted Answer

$$0$$

Question 9

Which of the following rational functions has NO horizontal asymptote?

Accepted Answer

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

Question 10

Given $$f(x) = \frac{4x^2$ + 1}{2x^2$ - 3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 11

If $$f(x) = \frac{2x^2$ + 1}{x^3$ + 2}$$, what is the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 12

For $$f(x) = \frac{3x^2$ + 2x + 1}{x^2$ - 1}$$, what is the behavior as $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o 3$$

Question 13

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

Accepted Answer

$$f(x) 	o 0$$

Question 14

Let $$f(x) = \frac{2x^3$ + 5x^2$ - 1}{x^2$ - 4}. As$$ $$x 	o -\infty$$, what is the end behavior?

Accepted Answer

$$f(x) \sim -2x$$

Question 15

Which of the following is true for $$f(x) = \frac{ax^n + \cdots}{bx^m + \cdots} as$$ $$x 	o \infty if$$ $$n = m$$?

Accepted Answer

$$f(x) 	o \frac{a}{b}$$

Question 16

For $$f(x) = \frac{2x^2$ + 3x + 1}{x^3$ + 1}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 17

If $$f(x) = \frac{3x^3$ + 2x^2$ + 1}{x^2$ - 1}$$, what is the end behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x) \sim 3x$$

Question 18

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

Accepted Answer

$$y = 2$$

Question 19

For $$f(x) = \frac{x^2$ + 1}{x^2$ - 1}$$, what is the behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 1$$

End Behavior and Asymptotes of Rational Functions in Business Calculus

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