Question 1

Which of the following best describes the domain and range of the exponential function $$f(x) = a^x$$ where $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

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

Question 2

The graph of $$f(x) = a^x$$ for $$a \u003e 1$$ passes through which key point?

Accepted Answer

$$(0, 1)$$

Question 3

What is the horizontal asymptote of the graph of $$f(x) = a^x$$ for $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

$$y = 0$$

Question 4

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

Accepted Answer

Its graph passes through $$(0, 1)$$ and has a horizontal asymptote at $$y = 0.$$

Question 5

If $$f(x) = 2^x$$ and $$g(x) = 2^x - 3$$, what is the horizontal asymptote of $$g(x)$$?

Accepted Answer

$$y = -3$$

Question 6

Which transformation is applied to the graph of $$f(x) = 3^x to $$obtain the graph of $$h(x) = 3^x - 1$$?

Accepted Answer

A vertical shift downward by 1 unit

Question 7

Given the equation $$4^x = 8$$, which method should be used to solve for $$x$$?

Accepted Answer

Rewrite both sides with the same base and equate the exponents

Question 8

What is the value of $$x$$ that solves the equation $$2^x = 16$$?

Accepted Answer

$$x = 4$$

Question 9

Which of the following is NOT a property of the graph of $$f(x) = a^x$$ for $$0 \u003c a \u003c 1$$?

Accepted Answer

The graph increases as $$x$$ increases

Question 10

If the graph of $$f(x) = 2^x is $$shifted up by 5 units, what is the new equation?

Accepted Answer

$$f(x) = 2^x + 5$$

Question 11

A population of bacteria doubles every hour. If the initial population is $$P_0$$, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2^t$$

Question 12

Which of the following best describes the effect of the transformation $$f(x) = a^x + k on $$the graph of $$f(x) = a^x$$?

Accepted Answer

It shifts the graph vertically by $$k$$ units

Question 13

The number $$e is $$defined as $$\lim_{n 	o \infty} \left(1 + \frac{1}{n}ight)^n. $$What is the approximate value of $$e$$?

Accepted Answer

$$2.718$$

Question 14

Which of the following is the correct domain and range for the natural exponential function $$f(x) = e^x$$?

Accepted Answer

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

Question 15

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 left by 1 unit

Question 16

Which of the following equations can be solved using the method of relating the bases?

Accepted Answer

$$9^x = 27$$

Question 17

If $$f(x) = 3^x$$ and $$h(x) = 3^x - 2$$, what is the $$y-$$intercept of $$h(x)$$?

Accepted Answer

$$-1$$

Question 18

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

Accepted Answer

The amount of a radioactive substance decreasing over time

Question 19

If $$f(x) = 5^x$$ and $$g(x) = 5$$^{-x}$$, how do the graphs of f(x$$)$$ and g(x$$)$$ compare?

Accepted Answer

The graph of $$g(x) is a $$reflection of $$f(x)$$ across the $$y-$$axis

Question 20

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

Accepted Answer

$$y = k$$

Exponential Functions: Definitions, Graphs, and Equations

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