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For each of the polynomial functions given, identify the leading term of the fun

ID: 3014810 • Letter: F

Question

For each of the polynomial functions given, identify the leading term of the function and describe the end behavior of the function based on your analysis of the leading term. a. f(x) = 2x^6 + 11x^9 - 13x^4 - 15x^3 Leading term: As x increases without bound, f(x) As x decreases without bound, f(x) b. g(x) = 2x(x - 11)(x - 13)(-15x + 6)^3 Leading term: As x increases without bound, g(x) As x decreases without bound, g(x) c. h(x) = 9x^3 + 3x - 13x^10 + 11 Leading term: As x increases without bound, h(x) As x decreases without bound, h(x) d. m(x) = -3(2 + x)(11x - 3)^2 Leading term: As x increases without bound, m(x) As x decreases without bound, m(x)

Explanation / Answer

a) f(x) = 11x^9 + 2x^6 -13x^4 -15x^3

Leading term : 11

odd degree polynomial

As x increases f(x) also increases : x---> inf ; f(x) ---> inf

x decreases f(x) also decreases: x--->- inf ; f(x) --->- inf

b) g(x) = 2x(x-11)(x- 13)(-15x+16)^3

Leading coefficient : 2*1*1*(-15)^3 = -6750

degree of g(x) = 6

As x increases/decreases g(x) always decreases

x---> +inf or x ---> -inf; g(x) ---> - inf