Quiz about APPC Rational Functions - Limits and End Behavior Quiz

Question 1

Evaluate the one-sided limit: $$\lim_{{x o 2^+}} \frac{1}{x-2}$$ .

Accepted Answer

$$+\infty$$

Answer

$$0$$

Answer

$$1$$

Answer

$$-\infty$$

Question 2

Evaluate the one-sided limit: $$\lim_{x o-3^-}\frac{2x-6}{x+3}$$ .

Accepted Answer

$$+\infty$$

Answer

$$0$$

Answer

$$1$$

Answer

$$-\infty$$

Question 3

Determine the end behavior of the rational function $$f(x) = \frac{3x^2 - x + 2}{x^2 + 1}$$ as $$x o \infty$$ .

Accepted Answer

$$3$$

Answer

$$0$$

Answer

$$1$$

Answer

$$+\infty$$

Question 4

Determine the end behavior of the rational function $$f(x) = \frac{5x^3 - 2x + 1}{2x^3 + 3x^2 - 1}$$ as $$x o -\infty$$ .

Accepted Answer

$$\frac{5}{2}$$

Answer

$$0$$

Answer

$$-\frac{5}{2}$$

Answer

$$-\infty$$

Question 5

Analyze the graph of the rational function $$f(x) = \frac{x^2 - 4}{x - 2}$$ . What is the behavior of $$f(x)$$ as $$x o 2$$ ?

Accepted Answer

$$f(x)$$ has a hole at $$x = 2$$

Answer

$$f(x)$$ has a vertical asymptote at $$x = 2$$

Answer

$$f(x)$$ approaches $$0$$ as $$x o 2$$

Answer

$$f(x)$$ approaches $$+\infty$$ as $$x o 2$$

Question 6

Evaluate the one-sided limit: $$\lim_{{x o 1^-}} \frac{x^2 - 1}{x - 1}$$ .

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$1$$

Answer

$$+\infty$$

Question 7

Determine the end behavior of the rational function $$f(x) = \frac{4x^4 - x^2 + 3}{2x^4 + x^3 - 5}$$ as $$x o \infty$$ .

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$4$$

Answer

$$+\infty$$

Question 8

Analyze the graph of the rational function $$f(x)=\frac{2x-4}{x^2-4}$$ . What is the behavior of $$f(x)$$ as $$x o2$$ ?

Accepted Answer

$$f(x)$$ has a hole at $$x = 2$$

Answer

$$f(x)$$ has a vertical asymptote at $$x = 2$$

Answer

$$f(x)$$ approaches $$0$$ as $$x o 2$$

Answer

$$f(x)$$ approaches $$+\infty$$ as $$x o 2$$

Question 9

Evaluate the one-sided limit: $$\lim_{{x o 0^+}} \frac{1}{x}$$ .

Accepted Answer

$$+\infty$$

Answer

$$0$$

Answer

$$1$$

Answer

$$-\infty$$

Question 10

Determine the end behavior of the rational function $$f(x) = \frac{6x^3 - x + 4}{3x^3 + 2x^2 - 1}$$ as $$x o -\infty$$ .

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$6$$

Answer

$$-\infty$$

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