End Behavior Extrema Sketching End Behavior Look left

End Behavior, Extrema & Sketching

End Behavior Look left and right, to figure out what’s happening up and down. right up or down left up or down

End Behavior: From a Graph 1. 2.

End Behavior: From a Graph 3. 4.

Determine the left and right behavior based on the equation. 5. f(x) = x 4 + 2 x 2 – 3 x 6. f(x) = -x 5 +3 x 4 – x 7. f(x) = 2 x 3 – 3 x 2 + 5

Tell me what you know about the equation… Odd exponent Positive leading coefficient

Tell me what you know about the equation… Even exponent Positive leading coefficient

Tell me what you know about the equation… Odd exponent Positive leading coefficient

Extrema are turns in the graph. • If you are given a graph take the turns and add 1 to get the least possible degree of the polynomial. • If you are given the function, take the degree and subtract 1 to get the extrema. f(x) = 2 x 3 – 3 x 2 + 5

8. What is the least possible degree of this function?

9. What is the least possible degree of this function?

What if you didn’t have a graph? 10. f(x) = x 4 + 2 x 2 – 3 x Number of Extrema: ____ 11. f(x) = -x 5 +3 x 4 – x Number of Extrema: ____ 12. f(x) = 2 x 3 – 3 x 2 + 5 Number of Extrema: ____

Sketching: # of Zeros: _____ Y-Int:

Sketching: # of Zeros: _____ Y-Int:

Homework: Worksheet ALL