Final answer:
The multiple zero of the function f(x) is x = 1 with a multiplicity of 2, and there is also a simple zero at x = -7 with a multiplicity of 1. Multiplicity affects how the graph interacts with the x-axis.
Step-by-step explanation:
The function f(x) = (x – 1)(x – 1)(x + 7) can be expressed as f(x) = (x – 1)2(x + 7). This indicates that there are two zeros or roots of the function: x = 1 and x = -7. The zero at x = 1 has a multiplicity of 2 because the factor (x – 1) appears twice. The zero at x = -7 has a multiplicity of 1 because the factor (x + 7) appears once. In graphing, the multiplicity indicates the behavior of the graph at the zero; an even multiplicity suggests the graph will touch and rebound off the x-axis, while an odd multiplicity implies the graph will cross the x-axis.