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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).

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

 x y -2 6 0 -6

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.

• A polynomial function will have repeated roots if one of the factors is repeated.
• The graph will be tangent to the x - axis at such points.

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

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