analyze the polynomial function fx3x3x43 adetermine the end

analyze the polynomial function f(x)=-3(x+3)(x+4)^3 a.)determine the end behavior of the graph of the function. b.) Find the x- and y- intercepts of the graph of the function c.) Determine the zeros of the function of the graph and their multiplicity.

Solution

a.)determine the end behavior of the graph of the function.

Leading term = negative
Degree = 4 = even

So, down on both sides

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b.) Find the x- and y- intercepts of the graph of the function

x-int :
-3(x + 3)(x +4)^3 = 0
x = -3 and -4

y-int :
Plug in x = 0
-3(0+3)(0+4)^3
-3(3)(64)
(0 , -576)

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Determine the zeros of the function of the graph and their multiplicity.

x = -3 and x = -4

x = -3 has multiplicity of 1
x = -4 has multiplicity of 3