Question 1

Which of the following best describes a rational function?

Accepted Answer

A function that can be written as the ratio of two polynomials.

Question 2

Given the rational function $$f(x) = \frac{2x+3}{x-1}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 1$$

Question 3

Which of the following is the correct end behavior of the rational function $$f(x) = \frac{3x^2$ + 2}{x^2$ - 5} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 3$$

Question 4

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

Accepted Answer

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

Question 5

Solve for $$x$$: $$2^x = 16$$

Accepted Answer

$$x = 4$$

Question 6

Which of the following is the inverse of the function $$f(x) = e^x$$?

Accepted Answer

$$f^{-1}(x$$) = \ln(x)$$

Question 7

If $$\log_3$(x) = 4$$, what is the value of $$x$$?

Accepted Answer

$$x = 81$$

Question 8

Which of the following is the solution to $$\log_2$(x) + \log_2$(x-2) = 3$$?

Accepted Answer

$$x = 4$$

Question 9

A population of bacteria doubles every 3 hours. If the initial population is 200, what is the population after 9 hours?

Accepted Answer

$$1600$$

Question 10

Which of the following is the correct formula for compound interest compounded annually?

Accepted Answer

$$A = P(1 + r)^t$$

Question 11

Solve for $$x$$: $$e^{2x} = 7$

Accepted Answer

$$x = \frac{1}{2} \ln(7)$$

Question 12

Which of the following is the horizontal asymptote of $$f(x) = 5e$$^{-x}$$ + 2$$?

Accepted Answer

$$y = 2$$

Question 13

If $$f(x) = \log_{10}(x)$$, what is $$f(1000)$$?

Accepted Answer

$$3$$

Question 14

Which of the following is the correct change of base formula for $$\log_b(a)$$?

Accepted Answer

$$\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$$

Question 15

A radioactive substance decays according to the formula $$A = A_0$ e$$^{-0.03t}$$. If the initial amount is 100 grams, how much remains after 10 years? (Round to two decimal places)

Accepted Answer

$$74.08$$ grams

Question 16

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b(x+y) = \log_b(x) + \log_b(y)$$

Question 17

Which of the following best describes the x-intercept of the exponential function $$f(x) = 2^x - 8$$?

Accepted Answer

$$x = 3$$

Question 18

If $$f(x) = \log_5$(x-1)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e 1$$

Question 19

A $$5000$$ investment grows at an annual rate of $$6\%$$ compounded continuously. What is the value after $$10$$ years? (Use $$A = Pe$$^{rt}$$ and round to the nearest dollar)

Accepted Answer

$$9025$$

Question 20

Which of the following equations models uninhibited exponential growth?

Accepted Answer

$$A = A_0$ e$$^{kt}$$

Study Guide: Rational, Exponential, and Logarithmic Functions (Chapters 3 & 4)

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