If a zero is of even multiplicity, then the graph of its function only touches the x–axis at that zero.
If a zero is of odd multiplicity, then the graph of its function crosses the x–axis at that zero.
How to identify the zero of a function?
If a solution or zero, has a multiplicity more than 1, namely appears there twice or more, like say (x - 3)³ = 0, that's:
(x - 3)(x - 3)(x - 3) = 0, and gives the zeros of:
x = 3, x = 3 and x =3.
Thus, it has a multiplicity of 3 in this case.
Now, if a zero has an EVEN multiplicity, like 2 or 4 or 8 or 12, the graph only hits the x-axis there, and bounces right back, it doesn't cross it, at that point.
If it has an ODD multiplicity, it does cross the x-axis at that point.
Complete question is:
If a zero is _______ then the graph of its function only touches the x–axis at that zero.
If a zero is _______, then the graph of its function crosses the x–axis at that zero.