Cc-26 Polynomial Functions Examples And Worksheet - Common Core Page 4
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8In general, the graph of a polynomial function of degree n (n Ú 1) has at most n - 1
turning points. The graph of a polynomial function of odd degree has an even number
of turning points. The graph of a polynomial function of even degree has an odd
number of turning points.
Problem 2
Describing End Behavior of Polynomial Functions
Consider the leading term of each polynomial function. What is the end behavior of
the graph? Check your answer with a graphing calculator.
3
4
3
2
A
B
y
4x
3x
y
2x
8x
8x
2
What do a and n
3
4
The leading term is -2x
The leading term is 4x
. Since n is odd
. Since n
represent?
and a is positive, the end behavior is
is even and a is negative, the end
a is the coefficient of the
down and up.
behavior is down and down.
leading term. n is the
exponent of the leading
Got It?
3
2
2. Consider the leading term of y = -4x
+ 2x
+ 7. What is the end behavior
term.
of the graph?
Problem 3
Graphing Cubic Functions
What is the graph of each cubic function? Describe the graph, including end behavior,
turning points, and increasing/decreasing intervals.
1
3
B
3
y
3x
x
A
y
x
2
Step 1
Step 2
Step 1
Step 2
How can you graph a
polynomial function?
y
4
x
y
Make a table of values
4
x
y
to help you sketch the
2
2
2
4
2
middle part of the graph.
Use what you know
1
2
1
0.5
x
x
about end behavior to
0
0
2
0
0
2
2
sketch the ends of the
1
2
graph.
1
0.5
2
2
2
4
4
4
Step 3
Step 3
The end behavior is up and down. There
The end behavior is down and up. There
are turning points at ( -1, -2) and (1, 2).
are no turning points. The function
The function decreases from -
to -1,
increases from -
to
.
increases from -1 to 1, and decreases
from 1 to
.
Got It?
3. What is the graph of each cubic function? Describe the graph.
3
2
3
a. y = -x
+ 2x
- x - 2
b. y = x
- 1
121
Lesson H-8 Polynomial Functions
121
CC-26 Polynomial Functions
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