# Graph Exponential Functions Worksheet

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}$

#### Solution:

The exponential function is of the form y = abx, where b > 0 and b ≠ 1 and x is any real number.

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$x$

#### Solution:

A function of the type y = abx, where b > 0 is an exponential function

The functions y = x2 and y = (x)6 / 5 are not in the form of y = abx.

So, they are not exponential functions.

The function y = (- 1 / 5)x is not an exponential function since b = - 1 / 5 < 0.

The function y = 2x is in the form of y = abx where b = 2 > 0.

So, it is an exponential function.

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

#### Solution:

A function of the type y = abx, where b > 0 is an exponential function

The function y = 4x is in the form of y = abx where a = 1, b = 4 > 0.

So, it is an exponential function.

The function y = (1 / 7)x is in the form of y = abx where a = 1, b = 1 / 7 > 0.

So, it is an exponential function.

The function y = (5 )- x = (1 / 5)x is in the form of y = abx where a = 1, b = 1 / 5 > 0.

So, it is an exponential function.

The function y = (- 6 / 5)x is not an exponential function since a = 1, b = - 6 / 5 < 0.

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.

#### Solution:

From the graph of the function, y = - (2x) is defined for all x values but only has y values that are less than 0.

The domain of y = - (2x) is the set of all real numbers and the range is the set of all negative numbers.

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$x$

#### Solution:

Substitute 0 for x in the equation y = -(4)-x.

y = - (4)-0
[Replace x with 0.]

= -40 = -1
[40 = 1.]

The point (0, -1) lies on the graph y = -(4)-x .

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$x$

#### Solution:

Substitute 3 for x in the equation y = 3 - x.

y = (3) - 3
[Replace x with 3.]

= 133 = 127
[Use the rules for negative exponents.]

The point (3, 1 / 27) lies on the graph y = 3 - x.

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$

#### Solution:

Check whether (2, 9 / 2) satisfies the equation y = 2(3 / 2)x.

y = 2 × (3 / 2)2
[Replace x with 2.]

= 2×3222
[Use power of a quotient property.]

= 9 / 2
[Simplify the fraction.]

So, the ordered pair (2, 9 / 2) is a solution of the exponential function, y = 2 (3 / 2)x.

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)$x$

#### Solution:

Substitute 0 for x in the equation y = - 4(6)x.

y = - 4 × (6)0
[Replace x with 0.]

= - 4 × 1 = - 4
[60 = 1.]

The point (0, - 4) lies on the graph of y = - 4(6)x.

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)$x$

#### Solution:

Substitute - 2 for x in the equation y = - (1 / 6)x.

y = - (16) - 2

= - (6 - 1) - 2 = - (62) = - 36
[Evaluate the power and multiply the factors.]

The point (- 2, - 36) lies on the graph of y = - (1 / 6)x.

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.

#### Solution:

From the graph of the function, y = (1 / 2)x is defined for all x values but only has y values that are greater than 0.

The domain of y = (1 / 2)x is the set of all real numbers and the range is the set of all positive real numbers.