Question 1

Which of the following is the correct definition of an exponential function?

Accepted Answer

A function of the form $$f(x) = b^x$$ where $$b \u003e 0$$ and $$b 
eq 1$$, and $$x is $$any real number.

Question 2

What is the domain and range of the exponential function $$f(x) = 2^x$$?

Accepted Answer

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

Question 3

Which property is true for the graph of $$f(x) = b^x$$ where $$b \u003e 1$$?

Accepted Answer

The graph passes through the point $$(0, 1).$$

Question 4

Given the function $$f(x) = e^x$$, which of the following statements is correct?

Accepted Answer

The graph of $$f(x)$$ lies between the graphs of $$f(x) = 2^x$$ and $$f(x) = 3^x.$$

Question 5

What is the value of $$e as $$defined in the study materials?

Accepted Answer

$$e = 2.71828$$

Question 6

Which of the following is the correct application of the Product Rule for Exponents?

Accepted Answer

$$a^m \cdot a^n = a$$^{m+n}$$

Question 7

If $$f(x) = 3^x$$, what is the horizontal asymptote of its graph?

Accepted Answer

$$y = 0$$

Question 8

Which transformation is applied to the graph of $$f(x) = 2^x to $$obtain $$g(x) = 2$$^{x}$$ - 4$$?

Accepted Answer

Vertical shift 4 units down

Question 9

Which rule allows you to simplify $$(a^m)^n$$?

Accepted Answer

Power Rule for Exponents

Question 10

What is the result of $$a^0$$ for any nonzero real number $$a$$?

Accepted Answer

$$a^0 = 1$

Question 11

Which of the following is the correct way to rewrite $$8^x$$ using base $$2$$?

Accepted Answer

$$8^x = 2$$^{3x}$$

Question 12

If $$f(x) = 2^x$$ and $$g(x) = 2$$^{x-1}$$, how is the graph of g(x$$)$$ related to the graph of f(x$$)$$?

Accepted Answer

It is shifted 1 unit to the right.

Question 13

Which of the following is the correct application of the Quotient Rule for Exponents?

Accepted Answer

$$\dfrac{a^m}{a^n} = a$$^{m-n}$$

Question 14

Which of the following is the correct way to express $$a^{-n}$$ for $$a 
eq 0$$?

Accepted Answer

$$a^{-n}$$ = \dfrac{1}{a^n}$$

Question 15

A biologist models the growth of a bacteria population with $$P(t) = 5 \cdot 2^t$$, where $$t is $$time in hours. What is the initial population?

Accepted Answer

$$5$$

Question 16

Which of the following is the correct definition of a rational exponent?

Accepted Answer

$$a^{m/n}$$ = (\sqrt[n]{a})^m$$

Question 17

Which of the following statements about the natural exponential function $$f(x) = e^x is $$true?

Accepted Answer

Its graph passes through $$(0, 1).$$

Question 18

If $$f(x) = 2^x$$ and $$g(x) = 2$$^{x}$$ + 3$$, what is the effect on the graph of $$f(x) to $$obtain $$g(x)$$?

Accepted Answer

Shift 3 units up

Question 19

Which of the following is the correct way to solve the equation $$2^x = 8 by $$rewriting the bases?

Accepted Answer

Rewrite $$8 as$$ $$2^3$$ and set $$x = 3$$

Exponential Functions: Properties, Graphs, and Equations

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