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Homework Check
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End Behavior, Extrema & Sketching
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Look left and right, to figure out what’s happening up and down.
End Behavior Look left and right, to figure out what’s happening up and down. right up or down up or down leftt
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End Behavior: From a Graph
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End Behavior: From a Graph
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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
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Tell me what you know about the equation…
Odd degree Positive leading coefficient
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Tell me what you know about the equation…
Page 261 #53 Even degree Negative leading coefficient
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Tell me what you know about the equation…
Page 261 #54 Odd degree Positive leading coefficient
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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 3rd degree, 2 extrema 4th degree, 3 extrema
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8. What is the least possible degree of this function?
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9. What is the least possible degree of this function?
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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: ____
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Sketching: # of Zeros: _________ Y-Int: ________ 1
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Sketching: # of Zeros: _________ Y-Int: ________
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Homework: Worksheet ALL
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