Math Problem Statement
For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of StartAbsoluteValue x EndAbsoluteValue .x.
f(x)equals=left parenthesis x minus 3 right parenthesis cubed(x−3)3left parenthesis x plus 1 right parenthesis squared(x+1)2
Type the power function that the graph of f resembles for large values of StartAbsoluteValue x EndAbsoluteValue .x.
yequals=enter your response here
Solution
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Math Problem Analysis
Mathematical Concepts
Polynomials
Zeros and Multiplicity
Turning Points
End Behavior
Formulas
End Behavior: Leading term dictates behavior for large |x|
Maximum Turning Points: n - 1 where n is the degree of the polynomial
Theorems
Multiplicity Theorem: Odd multiplicity means the graph crosses the x-axis, even multiplicity means it touches the x-axis
Polynomial Degree Theorem: The degree determines maximum turning points
Suitable Grade Level
Grades 10-12
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