Objectives:1. Be able to graph the exponential growth parent function.

2. Be able to graph all forms of the exponential growth function

Critical Vocabulary:Exponential, Asymptote

Warm Up: Evaluate each expression for x = 3 and x = -2 (NO DECIMAL ANSWERS)1. 3x 2. 6•3x 3. 2x + 5

I. Exponential Growth Function

Graph: f(x) = 2x

x

f(x)

0 1 2 3 4-1-2-3-4

Parent Function: f(x) = bx, where b > 1

Asymptote: A line that a graph gets closer and closer to but

never touches

Where is the Asymptote?

What is the Domain?

What is the Range?

f(x)= 2x versus f(x) = -2x

REFLECTIONS!!!!

f(x)= 2x versus f(x) = 3•2x

The graph increased quicker!!!!

f(x)= 2x versus f(x) = ½•2x f(x)= 2x versus f(x) = 2x+1

All points shifted left 1!!!!The graph increased slower!!!!

I. Exponential Growth Function

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

All points shifted up 1!!!!All points shifted right 1!!!!

f(x)= 2x versus f(x) = 2x - 1All points shifted down 1!!!!

I. Exponential Growth Function

f(x) = abx-h + k

a: Determines size and directions

Positive: increases left to right

Negative: decreases left to right

lal > 1: Changes quicker

lal < 1: Changes slower

lal = 1: Parent rate of change

h: Shifts the graph left or right

k: Shifts the graph up or down

Example 1: f(x) = -5•2x+3 – 2

•Reflects

•Quick change

•Shifts L3

•Shifts D2

Example 2: f(x) = 2x-4

•Asymptote: y = -2

Directions: List the characteristics of each exponential growth function

Example 3: f(x) = -½•2x + 4

Example 4: f(x) = -5•2x-2 - 7

I. Exponential Growth Function

Objectives:1. Be able to graph the exponential DECAY parent function.2. Be able to graph all forms of the exponential functions

(Growth and Decay)

Critical Vocabulary:Exponential, Asymptote

Warm Up: List the 5 characteristics of f(x) = -¼•2x-5 - 6

II. Exponential Decay Function

x

f(x)

0 1 2 3 4-1-2-3-4

Asymptote: A line that a graph gets closer and closer to but

never touches

Where is the Asymptote?

What is the Domain?

What is the Range?

Graph: f(x) = ½x

Parent Function: f(x) = bx, where 1 > b > 0

f(x)= ½x versus f(x) = -½x

REFLECTIONS!!!!f(x)= ½x versus f(x) = 3• ½x

The graph decreased quicker!!!!

II. Exponential Decay Function

f(x)= ½x versus f(x) = ½• ½x f(x)= ½x versus f(x) = ½x+1

All points shifted left 1!!!!The graph decreased slower!!!!

f(x)= ½x versus f(x) = ½x-1 f(x)= ½x versus f(x) = ½x + 1All points shifted up 1!!!!All points shifted right 1!!!!

II. Exponential Decay Function

f(x)= ½x versus f(x) = ½x - 1

All points shifted down 1!!!!

f(x) = abx-h + k

a: Determines size and directions

Positive: increases left to right

Negative: decreases left to right

lal > 1: Changes quicker

lal < 1: Changes slower

lal = 1: Parent rate of change

h: Shifts the graph left or right

k: Shifts the graph up or down

II. Exponential Decay Function

III. Graphing an Exponential Growth and Decay Function

Example 5: Graph: f(x) = 2•4x+2 + 1

•No reflection•Quick Change•Shifts L2•Shifts U1

x

f(x)

-2

3

-1

9

0

33

-3

3/2

-4

9/8

Domain: All Real Numbers

Range: y > 1

•Asymptote: y = 1

SPECIAL NOTE: When creating your table, the number in the middle (-2) will be whatever value of x would make the exponent turn into zero.

Exponential Growth

Example 6: Graph: f(x) = 2•½ x-1 + 2

•____________________x

f(x)

Domain: ____________

Range: _____________

III. Graphing an Exponential Growth and Decay Function

•____________________•____________________•____________________•____________________

Type: _________________

Page 482 #3-23 odds (11 problems)

Directions: All Graphs require characteristics, domain and range

Page 489 #3-21 odds (10 problems)