CCA2 Aim 22 end behavior.notebook
October 19, 2016
HW: Aim 22 Worksheet and prep for tomorrow's quiz on Aims 18-21
Aim #22: How do we determine the end behavior of a polynomial?
2
Kickoff: Sketch the graph of f(x) = x .
4
6
= x 2
f(x) h(x) = x 6
g(x) = x 4
Predict what the graph of f(x) = x and f(x) = x will look like.
Sep 4­9:27 PM
End Behavior
As x approaches infinity,
f(x) approaches
As x approaches infinity,
f(x) approaches
As x approaches negative
infinity, f(x) approaches
As x approaches negative
infinity, f(x) approaches
Sep 26­3:46 PM
1
CCA2 Aim 22 end behavior.notebook
October 19, 2016
3
Sketch the graph of f(x) = x .
5
7
= x3
f(x) = x 5
f(x)
f(x) = x 7
Predict what the graphs of f(x) = x and f(x) = x will look like.
Sep 26­5:00 PM
3
Sketch a graph of f(x) = -x . State the end behavior.
As x approaches infinity,
f(x) approaches
As x approaches infinity,
f(x) approaches
As x approaches negative
infinity, f(x) approaches
As x approaches negative
infinity, f(x) approaches
Sep 26­3:46 PM
2
October 19, 2016
Negative Leading Coefficient
Positive Leading Coefficient
CCA2 Aim 22 end behavior.notebook
Sep 26­5:11 PM
Real World Application:
The Center for Transportation Analysis (CTA) studies all aspects of transportation in the United States, from energy and environmental concerns to safety and security challenges. A 1997 study compiled the following data of the fuel economy in miles per gallon (mpg) of a car or light truck at various speeds measured in miles per hour (mph). The data is compiled in the table below. A scatter plot of the data is also shown. a. This data can be modeled by a polynomial function.
Determine if the function that models the data would have
an even or odd degree.
b. Is the leading coefficient of the polynomial that can be
used to model this data positive or negative?
Sep 26­5:12 PM
3
CCA2 Aim 22 end behavior.notebook
October 19, 2016
4
3
2
Model Problem: Consider the function f(x) = 2x + x - x + 5x + 3.
Predict its end behavior.
Graph the function on the calculator to check your prediction.
Sep 26­5:15 PM
5
4
3
2
Try: Consider the function f(x) = 2x - x - 2x + 4x + x + 3.
Predict its end behavior.
Graph the function on the calculator to check your prediction.
Sep 26­5:15 PM
4
CCA2 Aim 22 end behavior.notebook
October 19, 2016
Try: Consider the function
Predict its end behavior.
Graph the function on the calculator to check your prediction.
Sep 26­5:15 PM
Feeling Fancy?
Can you sketch a graph of an even degree polynomial function that
has no x-intercepts?
Can you sketch a graph of an odd degree polynomial function that
has no x-intercepts?
Sep 4­9:34 PM
5
CCA2 Aim 22 end behavior.notebook
October 19, 2016
PUTTING IT ALL TOGETHER!
For the polynomial 1) Find the zeros (or the x­intercepts) of f(x)
2) What is the multiplicity of each zero?
3) What is the y­intercept of f(x)?
4) What is the end behavior of f(x)?
5) Sketch a graph of f(x). Oct 10­4:26 PM
Post Game Report
The end behavior for a polynomial function is determined by the
degree of the polynomial:
• if the degree is even, the end behavior is the same as x
approaches infinity and negative infinity
• if the degree is odd, the end behavior is different as x
approaches infinity and negative infinity
• the graphs of odd degree functions have at least one x-intercept
• the graphs of even degree functions may not have an x-intercept
Sep 5­5:08 PM
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