SKETCH THE GRAPH OF THE EXPONENTIAL FUNCTION

Graph the exponential function.

Problem 1 :

Solution:

If x = -2,

y = (1/5)^-2 = 25

If x = -1,

y = (1/5)^-1 = 5

If x = 0,

y = (1/5)⁰ = 1

If x = 1,

y = (1/5)¹ = 0.2

If x = 2,

y = (1/5)² = 0.04

Asymptote:

Horizontal asymptote: y = 0

Problem 2 :

Solution:

If x = -2,

y = 2(1/2)^-2

y = 8

If x = -1,

y = 2(1/2)^-1

y = 4

If x = 0,

y = 2(1/2)⁰

y = 2

If x = 1,

y = 2(1/2)¹

y = 1

If x = 2,

y = 2(1/2)²

y = 0.5

Asymptote:

Horizontal asymptote: y = 0

Problem 3 :

Solution:

If x = 3,

y = (1/3)^3-5

= (1/3)^-2

y = 9

If x = 4,

y = (1/3)^4-5

= (1/3)^-1

y = 3

If x = 5,

y = (1/3)^5-5

= (1/3)⁰

y = 1

If x = 6,

y = (1/3)^6-5

= (1/3)¹

y = 0.33

If x = 7,

y = (1/3)^7-5

= (1/3)²

y = 0.11

Asymptote:

Horizontal asymptote: y = 0

Problem 4 :

Solution:

If x = -2,

y = (1/2)^-2 - 1

y = 3

If x = -1,

y = (1/2)^-1 - 1

y = 1

If x = 0,

y = (1/2)⁰ - 1

y = 0

If x = 1,

y = (1/2)¹ - 1

y = -0.5

If x = 2,

y = (1/2)² - 1

y = -0.75

Asymptote:

Horizontal asymptote: y = -1

Sketch the graph of each function. Then, state the domain, range and y-intercept, and change of y-values of the function.

Problem 5 :

Domain:

Range:

Y-intercept:

Growth or Decay?

Solution:

Domain: 

All real numbers

Range:

(-∞, 0)

y-intercept:

x = 0

y = -6(1/2)⁰

= -6(1)

y = -6

(0, -6)

Growth or Decay?

Growth

Problem 6 :

y =  0.5^x

Solution:

Domain: 

All real numbers

Range:

(0, ∞)

y-intercept:

x = 0

y = (0.5)⁰

y = 1

(0, 1)

Growth or Decay :

Decay

Problem 7 :

Solution:

Domain: 

All real numbers

Range:

(0, ∞)

y-intercept:

x = 0

y = 7/2(2)⁰

= 7/2(1)

y = 7/2

(0, 7/2)

Growth or Decay?

Growth

Problem 8 :

Solution:

Domain: 

All real numbers

Range:

(0, ∞)

y-intercept:

x = 0

y = 8(1/2)⁰

= 8(1)

y = 8

(0, 8)

Growth or Decay?

Decay

Problem 9 :

Graph the exponential function

Solution:

Match the function with its graph.

Problem 10 :

Solution:

By observing graph B, we get the horizontal asymptote y = 4

So, graph (B) is correct.

Problem 11 :

Solution:

By observing graph C, the parent function should be moved 4 units to the left. So, graph C is correct.

Problem 12 :

Solution:

By observing graph A, the parent function should be moved 4 units to the right. So, graph A is correct.