# FIND THE DOMAIN AND RANGE OF A EXPONENTIAL FUNCTION WORKSHEET

Find:

1) Domain

2) Range

3) Exponential growth or decay

4) Horizontal asymptote

Problem 1 :

f(x) = 3x

Solution

Problem 2 :

f(x) = -(3x)

Solution

Problem 3 :

f(x) = 3-x

Solution

Problem 4 :

f(x) = (1/3)x

Solution

Problem 5 :

f(x) = 2x - 3

Solution

Problem 6 :

f(x) = 2x-3

Solution

Problem 7 :

f(x) = 2x+5 - 5

Solution

Problem 8 :

f(x) = -2-x

Solution

Problem 9 :

f(x) = -2x+3 + 1

Solution

Problem 10 :

f(x) = (1/2)x-3 - 4

Solution

1)  f(x) = 3x

Domain:

The domain is all real number.

(-∞, ∞)

Range:

The range is all positive real numbers.

(0, ∞)

Exponential growth or decay:

exponential growth function.

Horizontal asymptote:

y = 0

2)  f(x) = -(3x)

Domain:

The domain is all real number.

(-∞, ∞)

Range:

The range is all negative real numbers.

(-∞, 0)

Exponential growth or decay:

it is reflection.

Horizontal asymptote:

y = 0

3)  f(x) = 3-x

Domain:

The domain is all real number.

(-∞, ∞)

Range:

The range is all positive real numbers.

(0, ∞)

Exponential growth or decay:

This is an exponential decay.

Horizontal asymptote:

y = 0

4)  f(x) = (1/3)x

Domain:

The domain is all real number.

(-∞, ∞)

Range:

The range is all positive real numbers.

(0, ∞)

Exponential growth or decay:

This is an exponential decay function.

Horizontal asymptote:

y = 0

5)  f(x) = 2x - 3

Domain:

The domain is all real number.

(-∞, ∞)

Range:

(-3, ∞)

Exponential growth or decay:

This is exponential growth function.

Horizontal asymptote:

y = -3

6)  f(x) = 2x-3

Domain:

The domain is all real number.

(-∞, ∞)

Range:

(0, ∞)

Exponential growth or decay:

This is an exponential growth function.

Horizontal asymptote:

y = 0

7)  f(x) = 2x+5 - 5

Domain:

The domain is all real number.

(-∞, ∞)

Range:

(-5, ∞)

Exponential growth or decay:

This is an exponential growth function.

Horizontal asymptote:

y = -5

8)   f(x) = -2-x

Domain:

The domain is all real number.

(-∞, ∞)

Range:

(-∞, 0)

Exponential growth or decay:

This is an exponential growth function.

Horizontal asymptote:

y = 0

9)  f(x) = -2x+3 + 1

Domain:

The domain is all real number.

(-∞, ∞)

Range:

(-∞, 1)

Exponential growth or decay:

This is an exponential decay function.

Horizontal asymptote:

y = 1

10)  f(x) = (1/2)x-3 - 4

Domain:

The domain is all real number.

(-∞, ∞)

Range:

(-4, ∞)

Exponential growth or decay:

This is an exponential decay function.

Horizontal asymptote:

y = -4

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