5-1 Activity: Investigating end behavior and turning points of polynomials
Expresión 26: "y" equals 2 "x" to the 4th power plus 2 "x" plus 2y=2x4+2x+2
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Expresión 27: "y" equals 3 "x" to the 4th power plus 3 "x" minus 1y=3x4+3x−1
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5. Describe the end behavior of the functions.
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The end behavior is up and up.
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6. How many turning points does each function have?
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Each function has one turning point.
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Part IV - 5th Degree Functions
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Expresión 33: "y" equals "x" to the 5th powery=x5
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Create two more functions with a degree of 5 where a is positive. Compare the three functions and answer the following questions.
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Expresión 35: "y" equals 3 "x" to the 5th power plus 2 "x" minus 1y=3x5+2x−1
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Expresión 36: "y" equals 2 "x" to the 5th power plus 3 "x" plus 2y=2x5+3x+2
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7. Describe the end behavior of the functions.
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The end behavior is up and down.
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8. How many turning points does each function have?
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Each function has zero turning points.
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Part V - Results
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9. What is the relationship between the degree of the function and the number of turning points?
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If the exponent is even, there will be one turning point, if the exponent is odd, there will be no turning point.
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10. Describe the end behavior of functions with an even degree.
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With an even degree, the end behavior will always be up and up.
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11. Describe the end behavior of functions with an odd degree.
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With an odd degree, the end behavior will allays be up and down.
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12. Describe how the sign of a (whether a is positive or negative) affects the end behavior of a function (You may have to graph some additional examples to confirm your answer).
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If a is negative, the end behavior will be up and down, if a is positive, the end behavior will be up and up.