Growth or Decay?
Writing Exponential Functions
Domain and Range
Transforming Exponential Functions
average rate of change
100
Is the following growth or decay: f(x) = 2x
Growth
100
Write the exponential function for this table:
x y
-2 1/9
-1 1/3
0 1
1 3
2 9
y=3x
100
The domain and range for f(x) = 2x
Domain (-infinity, infinity)
Range (0,infinity)
100
Describe the transformation in the following function:
f(x) = 2x
g(x) = 2x +5
Translated up 5 units
100
The average rate of change of f(x) = 2x over the interval (0, 3)
7/3
200
Is the following growth or decay: f(x)=100(0.5)x
Decay
200
Write an exponential equation for the table.
x y
-2 - 1/4
-1 - 1/2
0 -1
1 -2
2 -4
f(x)=-(2)x
200
The domain and range for f(x) = 3x - 4
domain (-infinity, infinity)
range (-4, infinity)
200
Describe the transformation in the following function:
f(x) = ex
g(x) = e(x+4)
Translated four units to the left
200
The average rate of change of f(x) = 3 (2)x over the interval (1,4)
14
300
Is the following growth or decay?
Decay
300
Write an exponential equation.
x y
-2 16
-1 4
0 1
1 1/4
2 1/16
y=(1/4)x
300
The domain and range for f(x) = 2 (4)x +1
Domain (-infinity, infinity)
Range (1, infinity)
300
Describe the transformation in the following function:
f(x) = 0.5x
g(x)= 0.5-x
Reflected over the y axis
300
The average rate of change of f(x) = 2x +3 over the interval (-2, 0)
3/8
400
Is the following growth or decay?
An electrical store calculates that the number of DVD players sold is decreasing by 13% per year.
Decay
400
Write an exponential equation.
x y
-2 9/4
-1 3/2
0 1
1 2/3
2 4/9
y=(2/3)x
400
The domain and range for f(x) = 5 (1/3)x -2
domain (-infinity, infinity)
range (-2, infinity)
400
Describe the transformations that took place:
BONUS: Can you write the equation?
Blue = 3x
Reflected over the x-axis, translated down 4 units
y= -3x-4
400
The average rate of change of f(x) = (1/3)x - 1 over the interval (0,2)
-4/9
500
The population of an ant colony increases at a rate of 44% per week.
Growth
500
Write an exponential equation.
x y
-2 -15/16
-1 -3/4
0 0
1 3
2 15
y=4x - 1
500
The domain and range for f(x) = -2 (4)x +3
domain (-infinity, infinity)
range (-infinity, 3)
500
Describe the transformations that took place:
BONUS: Can you write the equation?
Blue = ex
Reflected over the x-axis, moved up 4, and dilated by 2
-2ex+4
500
The average rate of change of f(x) = 3(2)x + 1 over the interval (-2, 2)
45/16