Graphs of Polynomial Functions - Kuta Software

Kuta Software - Infinite Precalculus

Name___________________________________

Graphs of Polynomial Functions

Date________________ Period____

For each function: (1) determine the real zeros and state the multiplicity of any repeated zeros, (2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph.

1) f (x)x

y

2) f (x)xx

y

x

x

3) f (x)xxxx

y

x

4) f (x)xx

y

x

-1-

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Worksheet by Kuta Software LLC

5) f (x)xxx

y

x

6) f (x)xx

y

x

Describe the end behavior of each function.

7) f (x)xxx

8) f (x)xx

9) f (x)xxx

10) f (x)xxx

11) f (x)xx

12) f (x)xx

Critical thinking questions:

13) Write a polynomial function f with the following properties: (a) Zeros at , , and

(b) f (x) for all values of x

(c) Degree greater than 1

14) Write a polynomial function g with degree

greater than one that passes through the

points (, ), (, ), and (, ).

-2-

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Precalculus

Name___________________________________

Graphs of Polynomial Functions

Date________________ Period____

For each function: (1) determine the real zeros and state the multiplicity of any repeated zeros, (2) list the x-intercepts where the graph crosses the x-axis and those where it does not cross the x-axis, and (3) sketch the graph.

1) f (x)x

y

Real zeros: mult. 3

x-int, crosses: x-int, doesn't cross: None

2) f (x)xx

y

Real zeros: mult. 2, x-int, crosses:

x-int, doesn't cross:

x

x

3) f (x)xxxx

y

Real zeros: , , ,

x-int, crosses: , , , x-int, doesn't cross: None

x

4) f (x)xx

y

Real zeros: mult. 3,

x-int, crosses: , x-int, doesn't cross: None

x

-1-

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Worksheet by Kuta Software LLC

5) f (x)xxx

y

Real zeros: mult. 3

x-int, crosses: x-int, doesn't cross: None

x

6) f (x)xx

y

Real zeros: mult. 2,

x-int, crosses: x-int, doesn't cross:

x

Describe the end behavior of each function.

7) f (x)xxx lim f (x)

x

lim f (x)

x

9) f (x)xxx lim f (x)

x

lim f (x)

x

11) f (x)xx lim f (x)

x

lim f (x)

x

Critical thinking questions:

13) Write a polynomial function f with the following properties: (a) Zeros at , , and

(b) f (x) for all values of x

(c) Degree greater than 1

f (x)(x)(x)(x)

8) f (x)xx lim f (x)

x

lim f (x)

x

10) f (x)xxx lim f (x)

x

lim f (x)

x

12) f (x)xx lim f (x)

x

lim f (x)

x

14) Write a polynomial function g with degree greater than one that passes through the

points (, ), (, ), and (, ). g(x)x(x)(x)

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-2-

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Worksheet by Kuta Software LLC

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