Question

Create a possible function, f(x), in factored form that could model the graph below. Give reasons or evidence to justify your answer. Use of graphing technology may assist you.

Answer 1

Given the graph of the function f(x)

We will write the equation of f(x) in factored form.

As shown, the zeros of the function are the points of the intersection with the x-axis.

there are 3 zeros: x = -3, x = 0, x = 4

So, the factors are: (x+3), x, (x-4)

There is a multiplicity of 2 for the factor (x+3)

So, the function will be:

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