Question

the function $f(x)=\frac{1}{8}x^{3}+3x^{2}-13x - 15$ is graphed below. what are its roots?
$x = {5, - 1,3}$
$x={-5,1,3}$
$x = {5,1,-3}$
$x={-5,-1,3}$

Explanation:

Step1: Recall root - definition

The roots of a function \(y = f(x)\) are the \(x\) - values for which \(f(x)=0\), i.e., the \(x\) - intercepts of the graph of the function.

Step2: Identify \(x\) - intercepts from graph

By looking at the graph of the function \(y=\frac{1}{8}x^{3}+3x^{2}-13x - 15\), the \(x\) - values where the graph crosses the \(x\) - axis are \(x=-5\), \(x = 1\), and \(x = 3\).

Answer:

\(x=\{-5,1,3\}\)