Question

the graph shows the zeros of the function. identify the multiplicity of each zero.

Explanation:

Step1: Analyze zero at $x=-3$

The graph touches the x-axis at $x=-3$ and turns around, which means the zero has an even multiplicity. The simplest even multiplicity is 2.

Step2: Analyze zero at $x=0$

The graph crosses the x-axis at $x=0$, which means the zero has an odd multiplicity. The simplest odd multiplicity is 1.

Step3: Analyze zero at $x=3$

The graph crosses the x-axis at $x=3$, which means the zero has an odd multiplicity. The simplest odd multiplicity is 1.

Answer:

• For zero $x=-3$: Multiplicity 2
• For zero $x=0$: Multiplicity 1
• For zero $x=3$: Multiplicity 1