Question 1

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

Accepted Answer

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

Question 2

What is the y-intercept of the function $$f(x) = a^x$$ for any $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

$$(0, 1)$$

Question 3

Which statement is true about the horizontal asymptote of $$f(x) = 3^x$$?

Accepted Answer

The horizontal asymptote is $$y = 0$$

Question 4

Amazon's revenue growth from 2000 to 2018 is best modeled by which type of function?

Accepted Answer

Exponential function

Question 5

Given $$f(x) = (\frac{1}{3})^x$$, which of the following is true about its behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x)$$ decreases toward zero

Question 6

What is the value of $$e as $$defined by the limit $$e = \lim_{n 	o \infty} (1 + \frac{1}{n})^n$$?

Accepted Answer

$$e = 2.71828\ldots$$

Question 7

Which transformation is applied to $$y = 3^x to $$obtain $$y = 3$$^{-x}$$ + 1$$?

Accepted Answer

Reflect about the y-axis and shift up 1 unit

Question 8

For the function $$f(x) = -e$$^{x+2}$$, what is the domain and range?

Accepted Answer

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

Question 9

Solve the exponential equation $$9^{2x-5} = 27^x$. What is the solution?

Accepted Answer

$$x = 10$$

Question 10

If $$f(x) = Ce$$^{kx}$$ models population growth, what does C$ represent?

Accepted Answer

The initial population

Question 11

Which property is true for all exponential functions $$f(x) = a^x$$ with $$a \u003e 1$$?

Accepted Answer

They are one-to-one and increasing

Question 12

What is the solution set for $$e^{-x^2}$$ = $$e^{5x-6}$$?

Accepted Answer

$$\{-6, 1\}$$

Question 13

Which of the following points is always on the graph of $$f(x) = a^x$$ for any $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

$$(0, 1)$$

Question 14

Which real-world scenario is best modeled by an exponential decay function?

Accepted Answer

The cooling of a hot object over time

Question 15

If $$f(x) = a^x$$ and $$0 \u003c a \u003c 1$$, which statement is true?

Accepted Answer

$$f(x) is a $$decreasing function

Question 16

What is the y-intercept of $$f(x) = 3$$^{-x}$$ + 1$$?

Accepted Answer

$$(0, 2)$$

Question 17

Which of the following is NOT a property of the exponential function $$f(x) = a^x$$ for $$a \u003e 1$$?

Accepted Answer

The function is decreasing

Question 18

If $$f(x) = Ce$$^{kx}$$ and k$$ \u003c 0$$, what type of behavior does the function exhibit?

Accepted Answer

Exponential decay

Question 19

Which of the following is the correct solution to the equation $$2^{x+1} = 8$?

Accepted Answer

$$x = 2$$

Question 20

If $$f(x) = 3^x$$ and $$g(x) = 3$$^{-x}$$, which statement is true?

Accepted Answer

$$g(x) is $$the reflection of $$f(x)$$ about the y-axis

Exponential Functions: Graphs, Properties, and Applications

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