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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 |