Which of the following could be the multiplicity of a zero whose graph crosses the x-axis?
Option #1: 2
Option #2: 3
Option #3: 4
Option # is the multiplicity.
All the options could be the multiplicity of a zero whose graph crosses the x-axis.
The multiplicity of a zero refers to the number of times a function crosses or touches the x-axis at a specific zero.
If the graph of a function crosses the x-axis at a zero, then the multiplicity of that zero could be any positive integer.
Therefore, all three options, 2, 3, and 4, could be the multiplicity of a zero whose graph crosses the x-axis.
The multiplicity of a zero is determined by the number of times its corresponding factor appears in the polynomial function. In this case, we are looking for a zero whose graph crosses the x-axis.
When a polynomial graph crosses the x-axis at a zero, the multiplicity of that zero is always odd. This means that option #2, with a multiplicity of 3, could be the multiplicity of a zero whose graph crosses the x-axis. Options #1 and #3, with multiplicities of 2 and 4 respectively, cannot correspond to zeros whose graphs cross the x-axis.
So the correct option is:
Option #2: 3