Question

Question 12 Multiple Choice Worth 1 points)(07.05 MC)1086Which of the following functions best represents the graph?fix)=(x-2)(x-3)(x+2)fx) = (x+2)(x+3)(x+12)f(x) = (x+2)(x+3)(x-2)1xx)=(x-2)(x-3)(x-12)

Answer 1

The graph of a function is given. It is required to find the function that represents the graph.

Notice from the graph that the function has roots or zeros at -3,-2, and 2.

Hence, the function takes the form:

$\begin{gathered} f(x)=a(x-(-3))(x-(-2))(x-2) \\ \Rightarrow f(x)=a(x+3)(x+2)(x-2) \end{gathered}$

Where a is a constant to be determined.

Notice that the given graph passes through the point (0,-12).

Substitute x=0 and f(x)=-12 into the equation of the function to find a:

$\begin{gathered} -12=a(0+3)(0+2)(0-2) \\ \Rightarrow-12=a(3)(2)(-2) \\ \Rightarrow-12=-12a \\ \text{ Swap the sides of the equation:} \\ \Rightarrow-12a=-12 \\ \text{ Divide both sides by }-12: \\ \Rightarrow\frac{-12a}{-12}=\frac{-12}{-12} \\ \Rightarrow a=1 \end{gathered}$

Hence, the function is:

$\begin{gathered} f(x)=1(x+3)(x+2)(x-2) \\ \Rightarrow f(x)=(x+2)(x+3)(x-2) \end{gathered}$

The third option is the answer: f(x)=(x+2)(x+3)(x-2).