Graph Exponential Functions Worksheet

**Page 1**

1.

Which of the following is the exponential function?

a. | $y$ = $\mathrm{ab}$ ^{$x$} where $b$ > 0 and $b$ ≠1 and $x$ is any real number | ||

b. | $y$ = $\mathrm{ax}$ ^{$b$} where $b$ > 0 and $x$ ≠ 0 | ||

c. | $y$ = $\mathrm{ax}$ ^{2} + $\mathrm{bx}$ | ||

d. | $y$ = $x$ ^{$\mathrm{ab}$} |

Correct answer : (1)

2.

Which of the following functions is an exponental function?

a. | $y$ = $x$ ^{2} | ||

b. | $y$ = ($x$) ^{ $\frac{6}{5}$ } | ||

c. | $y$ = (- $\frac{1}{5}$ ) ^{$x$} | ||

d. | $y$ = 2 ^{$x$} |

The functions

So, they are not exponential functions.

The function

The function

So, it is an exponential function.

Correct answer : (4)

3.

Which of the following functions is not an exponential function?

a. | $y$ = 4 ^{$x$} | ||

b. | $y$ = ($\frac{1}{7}$) ^{$x$} | ||

c. | $y$ = 5 ^{- $x$} | ||

d. | $y$ = (- $\frac{6}{5}$) ^{$x$} |

The function

So, it is an exponential function.

The function

So, it is an exponential function.

The function

So, it is an exponential function.

The function

Correct answer : (4)

4.

Use the graph shown to find the domain and the range of the function. $y$ = - (2^{$x$}).

a. | domain is set of all real numbers and the range is set of all negative numbers. | ||

b. | domain is set of all real numbers and the range is set of all positive numbers. | ||

c. | domain is set of all positive numbers and the range is set of all real numbers. | ||

d. | domain is set of all negative numbers and the range is set of all negative numbers. |

The domain of

Correct answer : (1)

5.

Identify the function that contains the point (0, - 1).

a. | $y$ = 4 ^{-$x$} | ||

b. | $y$ = -(4) ^{-$x$} | ||

c. | $y$ = 4 ^{$x$} | ||

d. | $y$ = 5 ^{$x$} |

[Replace

= -4

[4

The point (0, -1) lies on the graph

Correct answer : (2)

6.

Identify the function that contains the point (3, $\frac{1}{27}$).

a. | $y$ = 3 ^{ - $x$} | ||

b. | $y$ = 3 · ($\frac{1}{3}$) ^{$x$} | ||

c. | $y$ = 3 · 3 ^{$x$} | ||

d. | $y$ = 3 ^{$x$} |

[Replace

=

[Use the rules for negative exponents.]

The point (3,

Correct answer : (1)

7.

The ordered pair (2, $\frac{9}{2}$) is a solution for which of the following exponential functions?

a. | $y$ = 3(2) ^{$x$} | ||

b. | $y$ = 2($\frac{3}{2}$) ^{$x$} | ||

c. | $y$ = 3($\frac{3}{2}$) ^{$x$} | ||

d. | $y$ = $\frac{3}{2}$$x$ |

[Replace

=

[Use power of a quotient property.]

=

[Simplify the fraction.]

So, the ordered pair (2,

Correct answer : (2)

8.

Identify the exponential function that contains the point (0, - 4).

a. | $y$ = - 4(6) ^{$x$} | ||

b. | $y$ = - 6(4) ^{$x$} | ||

c. | $y$ = 4(6) ^{$x$} | ||

d. | $y$ = (6) ^{$x$} |

[Replace

= - 4 × 1 = - 4

[6

The point (0, - 4) lies on the graph of

Correct answer : (1)

9.

Identify the exponential function that contains the point (- 2, - 36).

a. | $y$ = ($\frac{1}{6}$) ^{$x$} | ||

b. | $y$ = - ($\frac{1}{6}$) ^{$x$} | ||

c. | $y$ = 6($\frac{1}{6}$) ^{$x$} | ||

d. | $y$ = - (6) ^{$x$} |

= - (6

[Evaluate the power and multiply the factors.]

The point (- 2, - 36) lies on the graph of

Correct answer : (2)

10.

Find the domain and the range of the function $y$ = ($\frac{1}{2}$)^{$x$} using the graph shown.

a. | domain is set of all negative numbers and the range is set of all negative numbers. | ||

b. | domain is set of all positive numbers and the range is set of all real numbers. | ||

c. | domain is set of all real numbers and the range is set of all real numbers. | ||

d. | domain is set of all real numbers and the range is set of all positive numbers. |

The domain of

Correct answer : (4)