Exponential Functions

1
Exponential Functions

• Exponential Growth
• Exponential Decay

2
Graph by creating a table of values
x y
-4
-2
0
1
2
3
0.0625
0.25
1
2
4
8
3
Graph by creating a table of values.
x y
-2
-1
0
2
4
6
4
2
1
0.25
0.0625
0.0156
4
Exponential Function

• b represents the beginning value
• b is also the y-intercept
• g represents the growth rate
• As g increases, the exponential curve gets
  steeper.
• As g decreases, the exponential curve flattens

5
Exponential Growth

• For the exponential function to be exponential
  growth, g gt 1.
• There is a horizontal asymptote at y k.
• Domain x can be all real numbers.
• Range
• If the curve goes upward, then the range is y gt
  k.
• If the curve goes downward, then the range is y lt
  k.

6
Exponential Decay

• For the exponential function to be exponential
  decay, g lt 1.
• There is a horizontal asymptote at y k.
• Domain is all real numbers.
• Range
• If b gt 0, then the range is y gt k.
• If b lt 0, then the range is y lt k.

7
Graph by creating a table of values.
x y
-2
-1
0
1
2
3
-0.25
-0.5
-1
-2
-4
-8
8
Graph by creating atable of values.
x y
-3
-2
-1
0
1
2
-8
-4
-2
-1
-0.5
-0.25
9
General Graph of Exponential Growth
h shifts the curve Right/Left
k shifts the curve Up/Down
10
Graph the Curve
11
Graph the Curve