To determine the zeros of the function [tex]\( f(x) \)[/tex] given its factors as [tex]\( (x-6) \)[/tex] and [tex]\( (x-1) \)[/tex], we follow these steps:
1. Identify the Factors of the Function:
The factors are given as [tex]\( (x-6) \)[/tex] and [tex]\( (x-1) \)[/tex].
2. Set Each Factor Equal to Zero and Solve for [tex]\( x \)[/tex]:
- For the factor [tex]\( (x-6) \)[/tex]:
[tex]\[
x - 6 = 0 \implies x = 6
\][/tex]
- For the factor [tex]\( (x-1) \)[/tex]:
[tex]\[
x - 1 = 0 \implies x = 1
\][/tex]
3. List the Zeros of the Function:
The values of [tex]\( x \)[/tex] that make each factor zero are known as the zeros of the function. Therefore, the zeros of the function are:
[tex]\[
x = 1 \text{ and } x = 6
\][/tex]
Given these steps, the correct answer is:
C. 1 and 6
