GRAPHING EXPONENTIAL GROWTH AND DECAY

To draw the graph of exponential growth and decay function, we should have the function as follows.

y = a b(x - h) + k 

Here y = k will be the horizontal asymptote. For the exponential function.

  • No vertical asymptote
  • domain is (-∞, ∞)
  • To find y-intercept, we can apply x = 0.

Graph and exponential function using the table provided. Then find the equation for the asymptote, and the function's domain and range.

Problem 1 :

f(x) = 2x

graphing-exponential-growth-and-decay-q1
graphing-exponential-growth-and-decay-q1-1

Asymptote : _____

Domain : _____

Range : _____

Solution :

Given, f(x) = 2x

f(x) = y

y = 2x

Let x = -3

y = 2-3

= 1/23

= 1/8

y = 0.125

Let x = -2

y = 2-2

= 1/22

= 1/4

y = 0.25

Let x = -1

y = 2-1

= 1/2

y = 0.5


Let x = 0

y = 20

y = 1

Let x = 1

y = 21

y = 2

Let x = 2

y = 22

y = 4

Let x = 3

y = 23

y = 8

x

-3

-2

-1

0

1

2

3

y

0.125

0.25

0.5

1

2

4

8

graphing-exponential-growth-and-decay-s1

Horizontal Asymptote : x axis or y = 0

Domain : (-∞, ∞)

Range : (0, ∞)

Problem 2 :

g(x) = 3(2x)

graphing-exponential-growth-and-decay-q2
graphing-exponential-growth-and-decay-q2-2

Asymptote : _____

Domain : _____

Range : _____

Solution :

Given, g(x) = 3(2x)

g(x) = y

y = 3(2x)

Let x = -3

y = 3(2-3)

= 3/23

y = 3/8

y = 0.375

Let x = 0

y = 3(20)

= 3/1

y = 3

Let x = -2

y = 3(2-2)

= 3/22

y = 3/4

y = 0.75

Let x = 1

y = 3(21)

y = 6


Let x = -1

y = 3(2-1)

= 3/21

y = 3/2

y = 1.5

Let x = 2

y = 3(22)

y = 12

Let x = 3

y = 3(23)

y = 24

x

-3

-2

-1

0

1

2

3

y

0.375

0.75

1.5

3

6

12

24

graphing-exponential-growth-and-decay-s2

Horizontal Asymptote : x axis or y = 0

Domain : (-∞, ∞)

Range : (0, ∞)

Problem 3 :

f(x) = (1/2)x

graphing-exponential-growth-and-decay-q3
graphing-exponential-growth-and-decay-q3-2

Asymptote : _____

Domain : _____

Range : _____

Solution :

Given, f(x) = (1/2)x

f(x) = y

y = (1/2)x

Let x = -3

y = (1/2)-3

= 23

y = 8

Let x = 0

y = (1/2)0

y = 1


Let x = -2

y = (1/2)-2

= 22

y = 4

Let x = 1

y = (1/2)1

y = 1/2

 y = 0.5

Let x = -1

y = (1/2)-1

= 21

y = 2

Let x = 2

y = (1/2)2

y = 1/4

 y = 0.25

Let x = 3

y = (1/2)3

y = 1/8

 y = 0.125

x

-3

-2

-1

0

1

2

3

y

8

4

2

1

0.5

0.25

0.125

graphing-exponential-growth-and-decay-s3

Horizontal Asymptote : x axis or y = 0

Domain : (-∞, ∞)

Range : (0, ∞)

Problem 4 :

g(x) = 2(x - 1)

graphing-exponential-growth-and-decay-q4
graphing-exponential-growth-and-decay-q4-2

Asymptote : _____

Domain : _____

Range : _____

Solution :

Given, g(x) = 2(x - 1)

g(x) = y

y = 2(x - 1)

Let x = -3

y = 2(-3 - 1)

= 2-4

= 1/24

= 1/16

y = 0.0625

Let x = 0

y = 2(0 - 1)

= 2-1

= 1/2

y = 0.5

Let x = -2

y = 2(-2 - 1)

= 2-3

= 1/23

= 1/8

y = 0.125

Let x = 1

y = 2(1 - 1)

= 20

y = 1


Let x = -1

y = 2(-1 - 1)

= 2-2

= 1/22

= 1/4

y = 0.25

Let x = 2

y = 2(2 - 1)

= 21

y = 2

Let x = 3

y = 2(3 - 1)

= 22

y = 4

x

-3

-2

-1

0

1

2

3

y

0.0625

0.125

0.25

0.5

1

2

4

graphing-exponential-growth-and-decay-s4

Horizontal Asymptote : x axis or y = 0

Domain : (-∞, ∞)

Range : (0, ∞)

Problem 5 :

f(x) = 3(4)x + 4

graphing-exponential-growth-and-decay-q5
graphing-exponential-growth-and-decay-q5-2

Asymptote : _____

Domain : _____

Range : _____

Solution :

Given, f(x) = 3(4)x + 4

f(x) = y

y = 3(4)x + 4

Let x = -3

y = 3(4)-3 + 4

y = 3 × 143 + 4= 3 × 164 + 4= 364 + 4

= 0.046875 + 4

y = 4.046875

Let x = 0

y = 3(4)0 + 4

= 3 + 4

y = 7

Let x = -2

y = 3(4)-2 + 4

y = 3 × 142 + 4= 3 × 116 + 4= 316 + 4

= 0.1875 + 4

y = 4.1875

Let x = 1

y = 3(4)1 + 4

= 12 + 4

y = 16

Let x = -1

y = 3(4)-1 + 4

y = 3 × 141 + 4= 3 × 14 + 4= 34 + 4

= 0.75 + 4 

y = 4.75

Let x = 2

y = 3(4)2 + 4

= 48 + 4

y = 52

Let x = 3

y = 3(4)3 + 4

=  192 + 4

y = 196

x

-3

-2

-1

0

1

2

3

y

4.046875

4.1875

4.75

7

16

52

196

graphing-exponential-growth-and-decay-s5

Horizontal Asymptote : y = 4

Domain : (-∞, ∞)

Range : (4, ∞)

Problem 6 :

g(x) = 2x - 2 - 3

graphing-exponential-growth-and-decay-q6
graphing-exponential-growth-and-decay-q6-2

Asymptote : _____

Domain : _____

Range : _____

Solution :

Given, g(x) = 2(x - 2) - 3

g(x) = y

y = 2(x - 2) - 3

Let x = -3

y = 2(-3 - 2) - 3

= 2-5 - 3

= 1/25 - 3

= 1/32 - 3

y = 0.03125 - 3

y = -2.96875

Let x = 0

y = 2(0 - 2) - 3

= 2-2 - 3

= 1/22 - 3

= 1/4 - 3

y = 0.25 - 3

y = -2.75

Let x = -2

y = 2(-2 - 2) - 3

= 2-4 - 3

= 1/24 - 3

= 1/16 - 3

y = 0.0625 - 3

y = -2.9375

Let x = 1

y = 2(1 - 2) - 3

= 2-1 - 3

= 1/21 - 3

= 1/2 - 3

y = 0.5 - 3

y = -2.5

Let x = -1

y = 2(-1 - 2) - 3

= 2-3 - 3

= 1/23 - 3

= 1/8 - 3

y = 0.125 - 3

y = -2.875

Let x = 2

y = 2(2 - 2) - 3

= 20 - 3

= 1 - 3

y = -2

Let x = 3

y = 2(3 - 2) - 3

= 21 - 3

= 2 - 3

y = -1

x

-3

-2

-1

0

1

2

3

y

-2.96875

-2.9375

-2.875

-2.75

-2.5

-2

-1

graphing-exponential-growth-and-decay-s6

Horizontal Asymptote :  y = -3

Domain : (-∞, ∞)

Range : (-3, ∞)

Recent Articles

RSS

  1. Finding Range of Values Inequality Problems

    May 21, 24 08:51 PM

    Finding Range of Values Inequality Problems

    Read More

  2. Solving Two Step Inequality Word Problems

    May 21, 24 08:51 AM

    Solving Two Step Inequality Word Problems

    Read More

  3. Exponential Function Context and Data Modeling

    May 20, 24 10:45 PM

    Exponential Function Context and Data Modeling

    Read More