1. End Behavior, Extrema & Sketching

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

3. End Behavior: From a Graph1. 2. 2.

4. End Behavior: From a Graph3. 3. 4.

5. 5. f(x) = x4 + 2x2 – 3x 6. f(x) = -x5 +3x4 – x 7. f(x) = 2x3 – 3x2 + 5
Determine the left and right behavior based on the equation.
5. f(x) = x4 + 2x2 – 3x
6. f(x) = -x5 +3x4 – x
7. f(x) = 2x3 – 3x2 + 5

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

7. Tell me what you know about the equation…
Page 261 #53
Even exponent
Positive leading coefficient

8. Tell me what you know about the equation…
Page 261 #54
Odd exponent
Positive leading coefficient

9. 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) = 2x3 – 3x2 + 5

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

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

12. What if you didn’t have a graph?
10. f(x) = x4 + 2x2 – 3x
Number of Extrema: ____
11. f(x) = -x5 +3x4 – x
Number of Extrema: ____
12. f(x) = 2x3 – 3x2 + 5
Number of Extrema: ____

13. Sketching:
# of Zeros: _________ Y-Int: ________

14. Sketching:
# of Zeros: _________ Y-Int: ________

15. Homework:
Worksheet
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