objectives: 1.be able to graph the exponential growth parent function. 2.be able to graph all forms...
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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)