End Behavior, Extrema & Sketching

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Presentation transcript:

End Behavior, Extrema & Sketching

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

End Behavior: From a Graph 1. 2. 2.

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

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

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

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

Tell me what you know about the equation… Page 261 #54 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) = 2x3 – 3x2 + 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) = x4 + 2x2 – 3x Number of Extrema: ____ 11. f(x) = -x5 +3x4 – x Number of Extrema: ____ 12. f(x) = 2x3 – 3x2 + 5 Number of Extrema: ____

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

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

Homework: Worksheet ALL