$$3 \times (1.5$$)^{-2}$$ = 3 \times \frac{1}{2.25} = 1.33$$

Question 1

Which of the following is an exponential function?

Accepted Answer

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

Question 2

Given the function $$f(x) = \left( \frac{1}{2} \right)^x$$, what is its domain?

Accepted Answer

$$x \in \mathbb{R}$$

Question 3

What is the horizontal asymptote of the function $$f(x) = 2^x$$?

Accepted Answer

$$y = 0$$

Question 4

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

Accepted Answer

$$(0, \infty)$$

Question 5

If $$f(x) = 3(1.5)^x$$, what is the value of $$f(-2)$$?

Accepted Answer

$$3 	imes (1.5$$)^{-2}$$ = 3 	imes \frac{1}{2.25} = 1.33$$

Question 6

Which of the following statements is true about the graph of $$f(x) = b^x$$ for $$0 \u003c b \u003c 1$$?

Accepted Answer

The graph decreases as $$x$$ increases.

Question 7

Evaluate $$f(x) = e^x at$$ $$x = -3. ($$Use $$e \approx 2.718)$$

Accepted Answer

$$e^{-3}$$ \approx 0.0498$$

Question 8

Which of the following functions represents exponential decay?

Accepted Answer

$$f(x) = \left( \frac{1}{3} \right)^x$$

Question 9

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

Accepted Answer

$$f(x) = 100 	imes 2^x$$

Question 10

Which of the following is NOT a property of exponential functions $$f(x) = b^x$$ with $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

The graph has a vertical asymptote at $$x = 0.$$

Question 11

Given $$f(x) = 10$$^{x+1}$$, what is the value of f(2$$)$$?

Accepted Answer

$$10^{2+1}$$ = $$10^3 = 1000$

Question 12

Which of the following best describes the effect of increasing the base $$b in$$ $$f(x) = b^x$$ for $$b \u003e 1$$?

Accepted Answer

The graph becomes steeper.

Question 13

If $$f(x) = e$$^{x-3}$$ - 1$$, what is the horizontal asymptote of the graph?

Accepted Answer

$$y = -1$$

Question 14

Which of the following is the correct base and power for the exponential function $$f(x) = 3(1.5)^x$$?

Accepted Answer

Base: $$1.5$$, Power: $$x$$

Question 15

Which of the following real-world scenarios can be modeled by an exponential function?

Accepted Answer

The amount of money in a bank account with continuous compounding interest.

Question 16

If $$f(x) = (-2)^x$$, is this an exponential function for all real $$x$$?

Accepted Answer

No, because the base is negative and $$(-2)^x is $$not defined for all real $$x.$$

Question 17

Evaluate $$f(x) = 2^x at$$ $$x = 3.14 ($$rounded to two decimal places).

Accepted Answer

$$2^{3.14}$$ \approx 8.82$$

Question 18

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

Accepted Answer

It is an exponential function with base $$e.$$

Question 19

If $$f(x) = \left( \frac{1}{2} \right)^x$$, what is $$f(-3)$$?

Accepted Answer

$$\left( \frac{1}{2} \$$right)^{-3}$$ = 8$$

Question 20

Which of the following best describes the end behavior of $$f(x) = 2^x as$$ $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o 0$$

Exponential Functions: Definitions, Properties, and Graphs

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