Graphing Polynomial Functions
Know vocabulary
1.) A ___________________________________ is a number, a variable, or a product of a number and a variable. The
variable does not have negative or fractional exponents.
2.) The ________________________________________ of a monomial in one variable is the exponent of the variable.
3.) A _________________________________________________ is a monomial or the sum or difference of monomials.
4.) A polynomial with one term is called a ______________________________________.
5.) A polynomial with two terms is called a _____________________________________.
6.) A polynomial with three terms is called a _____________________________________.
7.) True or False.
( )
8.) True or False.
( )
is a polynomial function.
√
9.) True or False
( )
10.) True or False
( )
is a polynomial function.
is a polynomial function.
is a polynomial function.
Recognizing graphs of Polynomial Functions
11.) True or False
The graph is a graph of a polynomial function.
12.) True or False
The graph is a graph of a polynomial function.
Recognizing graphs of Polynomial Functions
13.) True or False
The graph is a graph of a polynomial function.
14.) True or False
The graph is a graph of a polynomial function.
( )
15.) True or False
is in standard form.
16.) What is the degree of ( )
?
17.) What is the degree of ( )
?
18.) What is the degree of ( )
(
19.) What is the degree of ( )
(
Degree = __________
)
( )
21.) What is the leading coefficient of
( )
22.) Write ( )
in standard form.
23.) Write ( )
(
)(
)
Degree = __________
)
20.) What is the leading coefficient of
(
Degree = __________
) in standard form.
Degree = __________
?
?
Leading Coefficient = __________
Leading Coefficient = __________
Zeros of Polynomial Functions
24.) True or False
A polynomial function of degree 5 can have at most 5 zeros.
25.) Find the zeros of ( )
26.) Find the zeros of ( )
27.) Find the zeros of ( )
(
)(
)(
)
28.) Use the graph to determine the zeros of ( )
29.) Use the graph to determine if the multiplicity of the zero at
30.) Match the equations to the correct graph
( ) (
) (
)
( ) (
)(
)
is even or odd?
Multiple Choice
31.) Use long division.
(
)
(
)
A)
B)
C)
D)
E)
None of these
32.) Use synthetic division.
A)
B)
C)
D)
E)
None of these
33.) Given the end behavior, determine whether the degree is even or odd and the sign of the leading
coefficient.
Degree: Even or Odd
Degree: Even or Odd
Leading coefficient: Positive or Negative
Leading coefficient: Positive or Negative
Degree: Even or Odd
Degree: Even or Odd
Leading coefficient: Positive or Negative
Leading coefficient: Positive or Negative
Multiple Choice
34.) What is the end behavior of the polynomial function ( )
35.) What is the end behavior of the polynomial function ( )
36.) What is the end behavior of the polynomial function ( )
37.) Which is the graph of ( )
(
)(
A)
B)
C)
D)
)?
38.) Sketch the graph of ( )
Step – Use the leading coefficient test to determine the end behavior of ( )
Step – Let x = 0; to find the y-intercept of the graph of ( ).
Step – Factor ( )
Step – Determine the multiplicity of each zero and use it to sketch each x-intercept as a touch-n-turn or a cross.
Step – Sketch the graph
39.) Sketch the graph of ( )
, given that (
) and (
) are factors.
Step – Use the leading coefficient test to determine the end behavior of ( )
Step – Let x = 0; to find the y-intercept of the graph of ( ).
Step – Factor ( )
Step – Determine the multiplicity of each zero and use it to sketch each x-intercept as a touch-n-turn or a cross.
Step – Sketch the graph
40.) Sketch the graph of ( )
, given that (
) and (
) are factors.
Step – Use the leading coefficient test to determine the end behavior of ( )
Step – Let x = 0; to find the y-intercept of the graph of ( ).
Step – Factor ( )
Step – Determine the multiplicity of each zero and use it to sketch each x-intercept as a touch-n-turn or a cross.
Step – Sketch the graph
41.) Sketch the graph of ( )
, given that (
) is a factor with multiplicity 2.
Step – Use the leading coefficient test to determine the end behavior of ( )
Step – Let x = 0; to find the y-intercept of the graph of ( ).
Step – Factor ( )
Step – Determine the multiplicity of each zero and use it to sketch each x-intercept as a touch-n-turn or a cross.
Step – Sketch the graph
42.) Sketch the graph of ( )
, given that (
) is a factor with multiplicity 3.
Step – Use the leading coefficient test to determine the end behavior of ( )
Step – Let x = 0; to find the y-intercept of the graph of ( ).
Step – Factor ( )
Step – Determine the multiplicity of each zero and use it to sketch each x-intercept as a touch-n-turn or a cross.
Step – Sketch the graph