Question 1

Which of the following rational functions has vertical asymptotes at $$x = 1$$ and $$x = -3$$?

Accepted Answer

$$f(x) = \dfrac{1}{(x-1)(x+3)}$$

Question 2

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

Accepted Answer

There is a vertical asymptote at $$x = -2$$ and a hole at $$x = 2$$

Question 3

For the function $$f(x) = \dfrac{2x}{x^2$-4}$$, what are the types of asymptotes?

Accepted Answer

Vertical at $$x = 2$$ and $$x = -2$$, horizontal at $$y = 0$$

Question 4

A government agency allocates $$11$$ million dollars for pollution removal. The cost to remove $$p$$ percent of pollutants is $$C(p) = \dfrac{20}{100-p}. $$What is the maximum percent of pollutants that can be removed with this budget?

Accepted Answer

$$p = 45\% ($$since $$C(p) = 11$$ when $$p = 45)$$

Question 5

What happens to the cost $$C(p) = \dfrac{20}{100-p} as$$ $$p$$ approaches $$100$$?

Accepted Answer

The cost becomes infinitely large

Question 6

If the average cost per laptop is given by $$C(x) = \dfrac{2000}{x} + 1200$$, where $$x is $$the number of laptops produced, what is the horizontal asymptote of $$C(x)$$?

Accepted Answer

$$y = 1200$$

Question 7

A patient receives a drug with concentration $$C(t) = \dfrac{7}{t+2} mg/L$$, where $$t is $$hours since administration. How long after administration will the concentration be $$1 mg/L$$?

Accepted Answer

$$t = 5$$ hours$$\ (1 = \dfrac{7}{t+2} \implies t+2=7 \implies t=5)$$

Question 8

For the function $$f(x) = \dfrac{3x^2$-4x+2}{x^2$-4}$$, what are the vertical asymptotes?

Accepted Answer

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

Question 9

A solution is made by mixing $$2 L of $$glucose with $$x L of $$water. The concentration is $$C(x) = \dfrac{2}{x+2}. $$What happens to the concentration as $$x$$ increases?

Accepted Answer

It approaches $$0$$

Question 10

Given $$C(x) = \dfrac{2000}{x} + 1200$$, how many laptops must be produced for the average cost to be $$1300$$?

Accepted Answer

$$x = 20$$

Question 11

Which of the following best describes the real-world meaning of the horizontal asymptote in $$C(x) = \dfrac{2000}{x} + 1200$$?

Accepted Answer

The average cost per laptop approaches $$1200 as $$more laptops are produced

Question 12

For $$f(x) = \dfrac{2x^2$-4}{x^2$-4}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 13

A patient’s blood drug concentration is $$C(t) = \dfrac{7}{t+2}. $$What is the concentration $$5$$ hours after administration?

Accepted Answer

$$1 mg/L$$

Question 14

Which of the following rational functions has a hole at $$x = 2$$?

Accepted Answer

$$f(x) = \dfrac{x-2}{x^2$-4}$$

Question 15

If $$C(p) = \dfrac{20}{100-p}$$, what is the domain of $$C(p) in $$the context of removing pollutants?

Accepted Answer

$$p \u003c 100$$

Question 16

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

Accepted Answer

$$y = 3$$

E6

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