Below is the graph of a polynomial function f with real coefficients. Use the gr

Question

Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph. (a) The function f is increasing over which intervals? Choose all that apply. (-infinity, -8) (-5, -1) (-8, -1) (3, 7) (7, 9) (9, infinity) (b) The function f has local maxima at which x-values? If there is more than one value, separate them with commas. (c) What is the sign of the leading coefficient of f? (d) Which of the following is a possibility for the degree of f? Choose all that apply. 4 5 6 7 8 9

Explanation / Answer

a) the function is increasing that is going up from

( -infinity , - 8 ) U ( -7 , -1 ) U ( 3, 7 ) U ( 9 , + infinity )

so ( -infinity , - 8 )   ( 3, 7 ) ( 9 , + infinity ) apply

b) local maxima is at

x = -8 , -1 , 7

c) since the polynomial is starting down and going up

leading coefficient is positive

d) since there are 6 x intercepts

with one intercept of multiplicity even

so the possible degree of polynomial is 7 , 9

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