1. Evaluate and Graph Polynomial Functions
Notes 5.2 (Day 4)
Evaluate and Graph Polynomial Functions

2. Critical points: Relative minimum –
The pit of a curve in a polynomial function
Relative maximum –
The peak of a curve in a polynomial function

3. Important!
The maximum number of curves a graph can make is one less than its degree.
What is the maximum number of curves each polynomial function can have?

4. Important!
The maximum number of curves a graph can make is one less than its degree.
What is the smallest possible degree of the polynomial function?

5. Leading coefficient:
The first number in the polynomial, once the polynomial is in standard form.

6. Polynomials of Even Degree
The “tails” of the graph will be going in the same direction
Will have an odd number of relative minimums and maximums
If the leading coefficient is positive, the “tails” of the graph with be pointing up ↑
If the leading coefficient is negative, the “tails” of the graph with be pointing down ↓
Hint: Think of a quadratic (parabola) makes a curve in which both tails go the same direction.

7. Polynomials of Odd Degree
The “tails” of the graph will be going in the same direction
Will have an even number of relative minimums and maximums
If the leading coefficient is positive, the “tail” on the left will be pointing down ↓ and the tail on the right will be pointing up ↑
If the leading coefficient is negative, the “tail” on the left will be pointing up ↑and the tail on the right will be pointing down ↓

8. Leading Coefficients

9. Which of these graphs could be the graph of a polynomial whose leading term is ?, ?, ?, ?, ?

10. New Concepts Infinity -∞, +∞ “Approaches” → Where the graph is going
Remember: f(x) is the same as y.

11. Directions:
Describe the end behavior of the polynomial function by completing these statements: f(x) →__?__ as x → -∞ and f(x) → __?__ as x → +∞.
f(x) →__?__ as x → -∞
This means, is y increasing or decreasing as you look at the left “tail” of your graph.
If the tail is pointing up, the ? is +∞, if the tail is pointing down, the ? is -∞.
Hint: The leading term is the key to success in these problems!

12. Describe the end behavior of the polynomial function by completing these statements: f(x) →__?__ as x → -∞ and f(x) → __?__ as x → +∞. Sketch the general shape of the polynomial function.

13. Describe the end behavior of the polynomial function by completing these statements: f(x) →__?__ as x → -∞ and f(x) → __?__ as x → +∞. Sketch the general shape of the polynomial function.

14. Homework: P
Graphing Polynomial Functions WS