1. 6.4 Polynomial Functions
Polynomial in one variable : A polynomial with only one variable
Leading coefficient: the coefficient of the term with the highest degree in a polynomial in one variable
Polynomial Function: A polynomial equation where the y is replaced by f(x)

2. State the degree and leading cofficient of each polynomial, if it is not a polynomial in one variable explain why.
1. 7x4 + 5x2 + x – 9
2. 8x2 + 3xy – 2y2
3. 7x6 – 4x3 + x-1
4. ½ x2 + 2x3 – x5

3. Evaluating Functions Evaluate f(x) = 3x2 – 3x +1 when x = 3
Find f(b2) if f(x) = 2x2 + 3x – 1
Find 2g(c+2) + 3g(2c) if g(x) = x2 - 4

4. End Behavior
Describes the behavior of the graph f(x) as x approaches positive infinity or negative infinity.
Symbol for infinity

5. End behavior Practice
f(x) as x
f(x) as x

6. End Behavior Practice
f(x) as x
f(x) as x

7. End Behavior Practice
f(x) as x
f(x) as x

8. The Rules in General

9. To determine if a function is even or odd
Even functions: arrows go the same direction
Odd functions: arrows go opposite directions
To determine if the leading coefficient is positive or negative
If the graph goes down to the right the leading coefficient is negative
If the graph goes up to the right then the leading coeffiecient is positive

10. The number of zeros Critical Points
zeros are the same as roots: where the graph crosses the x-axis
The number of zeros of a function can be equal to the exponent or can be less than that by a multiple of 2.
Example a quintic function, exponent 5, can have 5, 3 or 1 zeros
To find the zeros you factor the polynomial
Critical Points
points where the graph changes direction.
These points give us maximum and minimum values
Relative Max/Min

11. Put it all together For the graph given Describe the end behavior
Determine whether it is an even or an odd degree
Determine if the leading coefficient is positive or negative
State the number of zeros

12. Cont… For the graph given Describe the end behavior
Determine whether it is an even or an odd degree
Determine if the leading coefficient is positive or negative
State the number of zeros

13. For the graph given Describe the end behavior
Determine whether it is an even or an odd degree
Determine if the leading coefficient is positive or negative
State the number of zeros

14. For the graph given Describe the end behavior
Determine whether it is an even or an odd degree
Determine if the leading coefficient is positive or negative
State the number of zeros