Question

Answer parts a through E for the function shown below

Answer 1

We are given the function

`f(x)=x^3+4x^2-x-4`

First, Let us do the simplification or factorization

`\begin{gathered} f(x)=x^2(x+4)-1(x+4) \\ f(x)=(x^2-1)(x+4) \\ f(x)=(x-1)(x+1)(x+4) \end{gathered}`

(a).

The coefficient of x^3 is positive

(b).

So basically, we set f(x) = 0 to get the x - intercepts

`\begin{gathered} f(x)=(x-1)(x+1)(x+4) \\ (x-1)(x+1)(x+4)=0 \\ x=1,-1,-4 \end{gathered}`

The x - intercepts are

`x=1, -1, -4`

The graph of f(x) is also given below