Question 1

Which of the following best describes an exponential function?

Accepted Answer

A function where the variable is in the exponent, such as $$f(x) = b^x$$

Question 2

Given the exponential function $$f(x) = 2^x$$, what is the y-intercept of its graph?

Accepted Answer

$$1$$

Question 3

Which of the following statements about the graph of $$f(x) = 3^x is $$TRUE?

Accepted Answer

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

Question 4

What is the domain of the logarithmic function $$f(x) = \log_2$(x)$$?

Accepted Answer

$$x \u003e 0$$

Question 5

Which of the following is the inverse of the function $$f(x) = 5^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_5(x$$)$$

Question 6

If the graph of $$f(x) = 2^x is $$reflected about the line $$y = x$$, what is the equation of the new graph?

Accepted Answer

$$f(x) = \log_2$(x)$$

Question 7

Which of the following best describes the range of the exponential function $$f(x) = 4^x$$?

Accepted Answer

$$y \u003e 0$$

Question 8

A scientist is studying bacteria growth modeled by $$N(t) = 100 \cdot 3^t$$, where $$t is in $$hours. How many bacteria will there be after 2 hours?

Accepted Answer

$$900$$

Question 9

Which transformation occurs when the graph of $$f(x) = e^x is $$changed to $$f(x) = e$$^{x-2}$$?

Accepted Answer

The graph shifts 2 units to the right

Question 10

If $$f(x) = \log_3$(x)$$, which of the following points lies on its graph?

Accepted Answer

$$(3, 1)$$

Question 11

Which of the following is the correct equation for the horizontal asymptote of $$f(x) = 2^x$$?

Accepted Answer

$$y = 0$$

Question 12

Which of the following statements is TRUE about the graph of $$f(x) = \log_2$(x)$$?

Accepted Answer

It has a vertical asymptote at $$x = 0$$

Question 13

A radioactive substance decays according to $$A(t) = 50 \cdot (0.8)^t. $$What is the amount left after 3 hours?

Accepted Answer

$$25.6$$

Question 14

Which of the following is the correct reflection of $$f(x) = 10^x$$ about the line $$y = x$$?

Accepted Answer

$$f(x) = \log_{10}(x)$$

Question 15

Which of the following best describes the relationship between exponential and logarithmic functions?

Accepted Answer

They are inverse functions of each other

Graphing Exponential and Logarithmic Functions – Step-by-Step Guidance

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