Question 1

Which of the following is an exponential function?

Accepted Answer

$$f(x) = 2^x$$

Question 2

What is the value of $$e ($$Euler's number) rounded to four decimal places?

Accepted Answer

$$e \approx 2.7183$$

Question 3

Which of the following describes the domain and range of the function $$f(x) = 3^x$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 4

Which transformation will reflect the graph of $$f(x) = 2^x$$ over the $$x-$$axis?

Accepted Answer

$$g(x) = -2^x$$

Question 5

Rewrite $$3^x = 81 in $$logarithmic form.

Accepted Answer

$$x = \log_3$ 81$$

Question 6

Evaluate $$\log_2$ 16.$$

Accepted Answer

$$4$$

Question 7

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

Accepted Answer

Product Rule

Question 8

Solve for $$x$$: $$2^x = 10 ($$round to two decimal places).

Accepted Answer

$$x \approx 3.32$$

Question 9

Which of the following is the correct change of base formula for $$\log_5$ 20$$?

Accepted Answer

$$\log_5$ 20 = \dfrac{\log_{10} 20}{\log_{10} 5}$$

Question 10

If $$f(x) = \log_2$(x-3)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(3, \infty)$$

Question 11

Which of the following equations is equivalent to $$\log_3$ x = 4$$?

Accepted Answer

$$x = 3^4$

Question 12

Which of the following best describes the range of $$f(x) = \log_5$ x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

Which transformation shifts the graph of $$f(x) = \log_2$ x$$ two units to the right?

Accepted Answer

$$g(x) = \log_2$ (x-2)$$

Question 14

Solve for $$x$$: $$\log_4$ (x+1) = 2.$$

Accepted Answer

$$x = 15$$

Question 15

Which of the following is the inverse of $$f(x) = 2^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_2 x$

Question 16

A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 2$$^{t/3}$$

Question 17

Which property of logarithms allows you to write $$\log_b \left(\dfrac{x}{y}\right) as$$ $$\log_b x - \log_b y$$?

Accepted Answer

Quotient Rule

Question 18

If $$f(x) = e^x$$, which of the following statements is true?

Accepted Answer

The graph passes through $$(0,1)$$ and increases as $$x$$ increases.

Question 19

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

Accepted Answer

$$x = 1.5$$

Inverse, Exponential, and Logarithmic Functions: Study Notes

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