2. Notes Over 3.2 Graphs of Polynomial Functions Continuous Functions Non-Continuous Functions Polynomial functions are continuous

3. Notes Over 3.2 Graphs of Polynomial Functions Rounded Turns Sharp Turns Polynomial functions have rounded turns

4. Notes Over 3.2 Graphs of Polynomial Functions Simplest Graphs of the Form: When n is oddWhen n is even

5. Notes Over 3.2 Sketching Transformations of Monomial Functions Left 2 Down

6. Notes Over 3.2 Sketching Transformations of Monomial Functions Down 1 Upwards

7. Notes Over 3.2 Leading Coefficient and Degree Test If leading coefficient is positive, it ends going up. If leading coefficient is negative, it ends going down If degree is odd, it starts and ends on opposites sides If degree is even, it starts and ends on the same side

8. Notes Over 3.2 Leading Coefficient and Degree Test If leading coefficient is positive, it ends going up. If leading coefficient is negative, it ends going down If degree is odd, it starts and ends on opposites sides If degree is even, it starts and ends on the same side Determine right-hand and left-hand behavior of each. – Because the leading coefficient is negative – Because the degree is odd (the opposite)– it falls to the right. it falls to the right. it rises to the left. it rises to the left.

9. Notes Over 3.2 Leading Coefficient and Degree Test If leading coefficient is positive, it ends going up. If leading coefficient is negative, it ends going down If degree is odd, it starts and ends on opposites sides If degree is even, it starts and ends on the same side Determine right-hand and left-hand behavior of each. – Because the leading coefficient is positive – Because the degree is even (the same)– it rises to the right. it rises to the right. it rises to the left. it rises to the left.

10. Goes straight through Bounces off point Notes Over 3.2 Zeros of a Polynomial Function Let n be the degree of the function. Then (n – 1) is the most turns the graph will have. n is the most number of zeros of the function (x-int). Find all of the zeros of the function, and use it to determine the number of turning points. Three turning points Three turning points

11. Goes through with curve Goes straight through Notes Over 3.2 Sketch the graph of the Polynomial Function Three turning points Three turning points it falls to the right. it falls to the right. it falls to the left. it falls to the left.

12. Goes straight through Bounces off Notes Over 3.2 Sketch the graph of the Polynomial Function Two turning points Two turning points it rises to the right. it rises to the right. it falls to the left. it falls to the left.

13. Notes Over 3.2 Writing Polynomial Function Find a polynomial with degree 4 that has the given zero.

14. Notes Over 3.2