Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{2x}{x^2$ - 4}$$?

Accepted Answer

All real numbers except $$x = 2$$ and $$x = -2$$

Question 2

Given $$f(x) = \frac{1}{x}$$, which of the following statements is TRUE about its graph?

Accepted Answer

It has vertical and horizontal asymptotes at $$x = 0$$ and $$y = 0$$

Question 3

For the function $$f(x) = \frac{2x}{x^2$ - 4}$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 0$$

Question 4

What is the vertical asymptote of the function $$f(x) = \frac{2x}{x^2$ - 4}$$?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 5

Which of the following is the horizontal asymptote for $$f(x) = \frac{2x}{x^2$ - 4}$$?

Accepted Answer

$$y = 0$$

Question 6

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

Accepted Answer

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

Question 7

For $$f(x) = \frac{1}{x}$$, which quadrant(s) does the graph occupy?

Accepted Answer

Quadrants I and III

Question 8

A rational function is defined as $$f(x) = \frac{P(x)}{Q(x)}. $$Which statement is correct regarding its domain?

Accepted Answer

The domain is all real numbers except where $$Q(x) = 0$$

Question 9

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

Accepted Answer

$$f(x)$$ approaches $$0$$

Question 10

If $$f(x) = \frac{2x}{x^2$ - 4}$$, what is the $$y-$$intercept?

Accepted Answer

$$y = 0$$

Question 11

Which of the following is NOT a characteristic of the reciprocal function $$f(x) = \frac{1}{x}$$?

Accepted Answer

It has a hole at $$x = 0$$

Question 12

Which real-world scenario can be modeled by a rational function similar to $$f(x) = \frac{1}{x}$$?

Accepted Answer

The intensity of light as distance from the source increases

Question 13

If $$f(x) = \frac{2x}{x^2$ - 4}$$, what is the behavior of $$f(x) as$$ $$x$$ approaches $$2$$?

Accepted Answer

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

Question 14

Which of the following is a correct statement about the horizontal asymptote of $$f(x) = \frac{2x}{x^2$ - 4}$$?

Accepted Answer

As $$x$$ approaches $$\pm\infty$$, $$f(x)$$ approaches $$0$$

Question 15

Which of the following best describes the graph of $$f(x) = \frac{1}{x}$$?

Accepted Answer

It is symmetric with respect to the origin

Rational Functions and Their Graphs: The Reciprocal Function

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