the graph of f(x) is given on the right. which roots of f(x) have an odd multiplicity? -1 1 3 done

Explanation:

Step1: Recall root - multiplicity property

If the graph of a polynomial function $y = f(x)$ crosses the $x$ - axis at a root $x = a$, then the root $a$ has an odd multiplicity. If the graph touches the $x$ - axis and turns around at a root $x = a$, then the root $a$ has an even multiplicity.

Step2: Analyze the graph at each root

At $x=-1$, the graph of $y = f(x)$ crosses the $x$ - axis. So, the root $x = - 1$ has an odd multiplicity. At $x = 1$, the graph of $y = f(x)$ touches the $x$ - axis and turns around. So, the root $x = 1$ has an even multiplicity. At $x = 3$, the graph of $y = f(x)$ crosses the $x$ - axis. So, the root $x = 3$ has an odd multiplicity.

Answer:

-1, 3