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Polynomial Functions Introduction

Investigating Polynomial Functions

Polynomial Division

Remainder & Factor Theorems

Polynomial Equations

Polynomial Inequalities

Rational Functions

Review&Test

 

jdsmathnotes

 

 


  UNIT 4 : POLYNOMIAL FUNCTIONS

 LESSON 8: POLYNOMIAL FUNCTIONS SUMMARY

 

 

 

End Behaviours of Polynomial Functions:

 

By the term end behaviors, we mean we are investigating the behavior of the function (y) as x takes on

larger and larger positive or negative values (increases without bound or decreases without bound).

 

 

 

 

 

 

 

 

 

 

 

 

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Cubic Functions in Factored Form: f(x) = k(x a)(x b)(x c)

 

 

x

y

-2

6

0

-6

 

 

 

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Cubic Functions in Factored Form with Repeated Factors: f(x) = k(x a)(x b)2

 

 

x

y

1

-4

 

Note: From the examples above we can make the following observations.

 

 

 

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 LESSON 5: POLYNOMIAL EQUATIONS

 

 

 

 

 LESSON 6: POLYNOMIAL INEQUALITIES

 

 

 

 

 

Interval

Test Number

- 4

- 2.5

0

3

Sign of (x + 3)

( - )

( + )

( + )

( + )

Sign of (x + 2)

( - )

( - )

( + )

( + )

Sign of (x 2)

( - )

( - )

( - )

( + )

Sign of (x + 3)(x + 2)(x 4)

( - )

( + )

( - )

( + )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 LESSON 7: RATIONAL FUNCTIONS

 

 

 

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Example:

 

x

y

0.5

2

0.9

90

1.1

111

1.5

6

2

2

 

 

 

 

 

 

 

x

y

-4

-6

-2

-2.5

5

-6

11

4

 

 

 

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