Question 1

Which of the following functions is an exponential function?

Accepted Answer

$$f(x) = 3^x$$

Question 2

Evaluate $$f(x) = 2^x$$ for $$x = 4. $$What is the value?

Accepted Answer

$$16$$

Question 3

Which of the following best describes the domain and range of the exponential function $$f(x) = e^x$$?

Accepted Answer

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

Question 4

The graph of $$f(x) = 2^x$$ has which of the following asymptotes?

Accepted Answer

$$y = 0$$

Question 5

If $$g(x) = 2$$^{x-3}$$ + 4$$, which transformation has been applied to the parent function $$f(x) = 2^x$$?

Accepted Answer

Shift right by 3 units and up by 4 units

Question 6

Which of the following is the logarithmic form of the exponential equation $$3^x = 81$$?

Accepted Answer

$$x = \log_3$ 81$$

Question 7

Evaluate $$\log_2$ 16$$ using properties of logarithms.

Accepted Answer

$$4$$

Question 8

Which property of logarithms allows you to write $$\log_b (xy) as$$ $$\log_b x + \log_b y$$?

Accepted Answer

Product Rule

Question 9

Rewrite $$\log_5$ 125$$ using the change of base formula.

Accepted Answer

$$\dfrac{\log 125}{\log 5}$$

Question 10

Solve the exponential equation $$4^x = 16$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 11

Which of the following is the equivalent exponential form of $$\log_3$ x = 5$$?

Accepted Answer

$$x = 3^5$

Question 12

Given $$f(x) = 2^x$$ and $$g(x) = \log_2$ x$$, which statement is true about their domains?

Accepted Answer

$$f(x)$$ has domain $$x \in \mathbb{R}$$, $$g(x)$$ has domain $$x \u003e 0$$

Question 13

Which graph transformation is applied to $$f(x) = e^x to $$obtain $$g(x) = e$$^{-x}$$ + 2$$?

Accepted Answer

Reflection over the $$y-$$axis and shift up by 2 units

Question 14

If $$\log_2$ x = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 15

Which of the following is the correct application of the power rule for logarithms to $$\log_3$ (x^4$)$$?

Accepted Answer

$$4 \log_3$ x$$

Question 16

A population of bacteria doubles every hour. If the initial population is 100, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 100 \cdot 2^t$$

Question 17

Which of the following is the correct logarithmic form of the equation $$e^x = 7$$?

Accepted Answer

$$x = \ln 7$$

Question 18

Condense the expression $$\log_2$ 8 + \log_2$ 4$$ into a single logarithm.

Accepted Answer

$$\log_2$ 32$$

Question 19

Expand $$\log_5$ \left(\dfrac{25x^3$}{y}\right)$$ using properties of logarithms.

Accepted Answer

$$2 \log_5$ 5 + 3 \log_5$ x - \log_5$ y$$

Question 20

Solve for $$x$$: $$2^{x+1} = 32$

Accepted Answer

$$x = 4$$

Study Guide: Inverse, Exponential, and Logarithmic Functions (Precalculus)

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