ANSWER and EXPLANATION
The multiplicity of a zero of a function is the number of times that the zero or its corresponding factor appears.
The zero located at x = 1 corresponds to the factor (x - 1). The factor appears twice in the function (since it is squared), hence, the zero located at x = 1 has a multiplicity of 2.
The zero located at x = -3 corresponds to the factor (x + 3) and this factor appears three times in the function. Hence, the zero located at x = -3 has a multiplicity of 3.
The graph of a function will touch and not cross the x-axis only at a zero that has an even multiplicity.
Hence, the graph of the function will touch, but not cross, the x-axis at an x-value of 1 only.
