Question 1

Which of the following best describes the domain and range of the exponential function $$y = 2^x$$?

Accepted Answer

Domain: $$x \in \mathbb{R}$$, Range: $$y \u003e 0$$

Question 2

What is the horizontal asymptote of the function $$y = 3^x + 2$$?

Accepted Answer

$$y = 2$$

Question 3

Which transformation results in a reflection of the graph of $$y = 2^x$$ over the $$x-$$axis?

Accepted Answer

$$y = -2^x$$

Question 4

If $$f(x) = 2^x$$, which equation represents a vertical stretch by a factor of 3?

Accepted Answer

$$f(x) = 3 \cdot 2^x$$

Question 5

Which of the following is the correct formula for continuously compounded interest?

Accepted Answer

$$A = Pe$$^{rt}$$

Question 6

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

Accepted Answer

$$x = 81$$

Question 7

Which property allows you to rewrite $$\log_b(MN) as a $$sum?

Accepted Answer

$$\log_b(MN) = \log_b(M) + \log_b(N)$$

Question 8

Solve for $$x$$: $$5^{2x} = 125$.

Accepted Answer

$$x = 1.5$$

Question 9

Which of the following is equivalent to $$\log_b(a^k)$$?

Accepted Answer

$$k \log_b(a)$$

Question 10

If $$f(x) = \log_2$(x)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e 0$$

Question 11

Which equation correctly converts the exponential equation $$2^x = 7 to $$logarithmic form?

Accepted Answer

$$x = \log_2$(7)$$

Question 12

A radioactive substance decays according to $$A = A_0$ e$$^{-kt}$$. If A_0$ = 100$$ grams and $$k = 0.2$$, how much remains after 5 hours?

Accepted Answer

$$A = 100 e$$^{-1}$$

Question 13

Which of the following statements about the graph of $$y = \log_b(x)$$ for $$b \u003e 1 is $$true?

Accepted Answer

It passes through $$(1, 0)$$ and increases to the right.

Question 14

Which transformation shifts the graph of $$y = e^x$$ three units to the left?

Accepted Answer

$$y = e$$^{x+3}$$

Question 15

If $$\log_5$(x) = 2$$, what is $$x$$?

Accepted Answer

$$x = 25$$

Question 16

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 17

Solve for $$x$$: $$3^{x+1} = 27$.

Accepted Answer

$$x = 2$$

Question 18

Which of the following best describes the end behavior of $$y = 2$$^{-x}$$ as x$$ 	o \infty$$?

Accepted Answer

$$y 	o 0$$

Question 19

If $$f(x) = \log(x)$$ and $$g(x) = e^x$$, what is $$f(g(x))$$?

Accepted Answer

$$x$$

Question 20

A population grows according to $$P(t) = 500e$$^{0.03t}$$. What is the population after 10 years?

Accepted Answer

$$P(10) = 500e$$^{0.3}$$

Exponential and Logarithmic Functions: Precalculus Study Guide

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