3. (10 points) Shown here is the graph of a polyno- mial function f( (a) Is the

Question

3. (10 points) Shown here is the graph of a polyno- mial function f( (a) Is the degree of this polynomial function even or odd? Explain how the graph indicates this. (b) Is the leading coefficient of the polynomial function positive or negative? Explain how the graph indicates this. (c) What is the value of the constant coefficient? Explain how the graph indicates this (d) Identify the real zeros of the polynomial function, and state whether the multiplicity of each zero is even or odd (e) Provide a possible function that could be represented by the graph. (Your answer will be checked by entering the function that you provide into a graphing tool and compared to the graph shown here.)

Explanation / Answer

a) degree of the function is even as both its ends are in same direction

b) leading coefficient is positive as its ends are upwards

c) value of cosntant coefficient is 1 /9

d) real zeros are x = -3 ( multiplicity odd ) , 1 ( multiplicity even ) , 3 ( multiplicity odd )

e) f(x) = a ( x+ 3) ( x-1)^2 ( x- 3)

-1 = a ( 3 ) ( -1 )^2 (-3)

-1 = -9a

a = 1/9

so, funation can be written as

f(x) = 1/9 ( x+ 3) ( x-1)^2 ( x- 3)

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