Question

Choose which function is represented by the graph.111032-11-10 9 8 7 6 5 4-3-2-102 3 4 5 6 7 8 9 10 1110O A. 1(x) = (x − 1)(x +2)(x+4)(x+8)B. f(x) - (x-8)(x-4)(x-2)(x+1)C. f(x)=(x-1)(x+2)(x+4)D. f(x)=(x-4)(x-2)(x+1)876544 4 4 & & To-2X

Answer 1

The factors of a polynomial tell us the points where the graph intersects the x-axis.

From the graph provided in the question, the graph cuts the x-axis at the points:

`x=-4,x=-2,x=1`

Therefore, the factors will be:

`\begin{gathered} x=-4,x+4=0 \\ x=-2,x+2=0 \\ x=1,x-1=0 \\ \therefore \\ factors\Rightarrow(x+4),(x+2),(x-1) \end{gathered}`

Therefore, the polynomial will be:

`f(x)=(x+4)(x+2)(x-1)`

OPTION C is the correct option.