Q: Given the rational function $$F(x) = \frac{x^2$ - 9}{x^2$ - 4}$$, which of the following best describes its domain?

$$\mathbb{R} \\backslash \\left\{ -2, 2 \\right\}$$

Q: Which of the following best describes the range of $$F(x) = \frac{1}{x}$$?

$$\mathbb{R} \\backslash \\left\{ 0 \\right\}$$

Question 1

Given the rational function $$F(x) = \frac{x^2$ - 9}{x^2$ - 4}$$, which of the following best describes its domain?

Accepted Answer

$$\mathbb{R} \backslash \left\{ -2, 2 \right\}$$

Question 2

Which of the following rational functions has a hole at $$x = 1$$?

Accepted Answer

$$F(x) = \frac{x^2$ - 1}{x - 1}$$

Question 3

What is the horizontal asymptote of the function $$F(x) = \frac{3x^2$ + 2}{x^2$ - 5}$$?

Accepted Answer

$$y = 3$$

Question 4

A chemical reaction's rate is modeled by $$R(x) = \frac{4x}{x^2$ + 1}. $$What is the range of $$R(x)$$?

Accepted Answer

$$\left( -2, 2 \right)$$

Question 5

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

Accepted Answer

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

Question 6

If $$F(x) = \frac{x^3$ - 8}{x^2$ - 4}$$, what is the end behavior of $$F(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$F(x) 	o \infty$$

Question 7

A rational function $$F(x)$$ has a numerator of degree 2 and a denominator of degree 3. What is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 8

Which of the following best describes the x-intercepts of $$F(x) = \frac{x^2$ - 4}{x^2$ - 1}$$?

Accepted Answer

$$x = -2, 2$$

Question 9

A rational function models the concentration of a drug in the bloodstream: $$C(t) = \frac{5t}{t^2$ + 1}. $$What is the maximum possible concentration?

Accepted Answer

$$2.5$$

Question 10

Given $$F(x) = \frac{x^2$ - 1}{x^2$ - 4}$$, which of the following statements is true?

Accepted Answer

There are vertical asymptotes at $$x = -2$$ and $$x = 2$$

Question 11

Which of the following rational functions has no horizontal asymptote?

Accepted Answer

$$F(x) = \frac{2x^3$ + 1}{x^2$ - 4}$$

Question 12

A rational function $$F(x)$$ has a vertical asymptote at $$x = 3$$ and a horizontal asymptote at $$y = 0. $$Which of the following could be $$F(x)$$?

Accepted Answer

$$F(x) = \frac{2x}{x - 3}$$

Question 13

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

Accepted Answer

$$\mathbb{R} \backslash \left\{ 0 \right\}$$

Question 14

If $$F(x) = \frac{x^2$ - 4}{x^2$ - 1}$$, what are the vertical asymptotes?

Accepted Answer

$$x = -1, 1$$

Question 15

A rational function $$F(x)$$ has a numerator and denominator of equal degree. What determines the horizontal asymptote?

Accepted Answer

The ratio of the leading coefficients

Question 16

Which of the following rational functions has a y-intercept at $$y = 0$$?

Accepted Answer

$$F(x) = \frac{x}{x + 1}$$

Question 17

A rational function $$F(x)$$ has a removable discontinuity (hole) at $$x = 2. $$Which of the following must be true?

Accepted Answer

Both the numerator and denominator have a factor of $$(x - 2)$$

Question 18

Which of the following rational functions has a slant (oblique) asymptote?

Accepted Answer

$$F(x) = \frac{x^2$ + 1}{x}$$

Question 19

A rational function $$F(x) is $$used to model the speed of a car as $$F(x) = \frac{60x}{x^2$ + 9}. $$What is the maximum speed the car can reach according to this model?

Accepted Answer

$$30$$

Rational Functions: Properties, Domain, Range, and Asymptotes

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