Coordinated Algebra Unit 3 Part B. What is an Exponential Function?
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Transcript of Coordinated Algebra Unit 3 Part B. What is an Exponential Function?
Coordinated AlgebraUnit 3 Part B
What is an Exponential Function?
Examples…
Applications…
Population Growth
Science (Bacterial Growth, Radiation, Half-Life,
etc.)
Investments/Finance
Appreciation and Depreciation
Let’s examine exponential functions. They are different than any of the other types of functions we’ve studied because the independent variable is in the exponent.
xxf 2
Let’s look at the graph of this function by plotting some points. x 2x
3 8 2 4 1 2 0 1
-1 1/2 -2 1/4 -3 1/8
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
2
121 1 f
Recall what a negative exponent means:
BASE
xxf 2
xxf 3
Compare the graphs 2x, 3x , and 4x
Characteristics about the Graph of an Exponential Function where a > 1 xaxf
What is the domain of an exponential function?
1. Domain is all real numbers
xxf 4
What is the range of an exponential function?
2. Range is positive real numbers
What is the x intercept of these exponential functions?
3. There are no x intercepts because there is no x value that you can put in the function to make it = 0
What is the y intercept of these exponential functions?
4. The y intercept is always (0,1) because a 0 = 1
5. The graph is always increasing
Are these exponential functions increasing or decreasing?
6. The x-axis (where y = 0) is a horizontal asymptote for x -
Can you see the horizontal asymptote for these functions?
xxf 2
xxf 3
xexf