1. Bell Ringer 1. What is a function? 2. What “test” can you use to determine if a graph is a function? 3. What is domain? 4. What is range?

2. Graphing Polynomial Functions Wednesday, March 16, 2016

3. Steps for Graphing Polynomial Functions 1. Find all zeros and plot the x-intercepts. 2. Determine end behavior and draw those segments. 3. Substitute zero for x to find the y-intercept and plot it. 4. Estimate the maxima and minima (aka turning points) using a graphing calculator and plot the turning points. A polynomial function degree n can have at most n-1 turning points. 5. Draw the rest of the function as a smooth curve.

4. How to determine End Behavior

5. Examples: list the 1) Zeros, 2) End Behavior, 3) y-intercept, 4) maxima and minima, 5) and sketch the graph. 1. f(x) = x 4 + x 3 – 4x 2 – 4x 2. f(x) = x 3 – 5x 2 + 3x + 2 3. f(x) = -x 4 – 7x 2 + x + 5 4. f(x) = -x 3 – x 2 + 1

6. Classwork and Homework Classwork: Algebra II book p. 356 #13-26 For each problem, list the 1) Zeros, 2) End Behavior, 3) y-intercept, 4) maxima and minima, 5) and sketch the graph. Homework: Graphing Polynomial Functions

7. Exit Ticket 1. Explain how to determine end behavior. 2. If a polynomial has 8 turning points, what is the least degree it could be?