4. Polynomial Functions
Understanding Polynomial Functions
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The given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points.
A
Right side rises; Ends are opposite & 4 maximum turning points
B
Right side rises; Ends are opposite & 5 maximum turning points
C
Right side rises; Ends are the same & 4 maximum turning points
D
Right side falls; Ends are opposite & 4 maximum turning points
Verified step by step guidance1
Identify the leading term of the polynomial, which is \(4x^5\). The leading term determines the end behavior of the polynomial.
Determine the degree of the polynomial. The degree is the highest power of \(x\) in the polynomial, which is 5 in this case.
Since the degree is odd (5), the ends of the polynomial will behave oppositely. This means one end will rise and the other will fall.
Examine the leading coefficient, which is 4. Since it is positive, the right side of the graph will rise.
Calculate the maximum number of turning points. The maximum number of turning points for a polynomial is one less than the degree, so for a degree of 5, there can be up to 4 turning points.
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