To determine if the function [tex]\( f(x) = x^2 - x + 8 \)[/tex] is an even function, you need to evaluate [tex]\( f(-x) \)[/tex] and compare it to [tex]\( f(x) \)[/tex].
1. Start by substituting [tex]\(-x\)[/tex] for [tex]\(x\)[/tex] in the function:
[tex]\[
f(-x) = (-x)^2 - (-x) + 8.
\][/tex]
2. Simplify the expression:
[tex]\[
(-x)^2 - (-x) + 8 = x^2 + x + 8.
\][/tex]
3. Now, compare [tex]\( f(-x) \)[/tex] with [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = x^2 - x + 8.
\][/tex]
[tex]\[
f(-x) = x^2 + x + 8.
\][/tex]
Clearly, [tex]\( f(-x) \neq f(x) \)[/tex].
Therefore, the function [tex]\( f(x) = x^2 - x + 8 \)[/tex] is not an even function.
From the given statements, the one that correctly describes the method is:
[tex]\[ \text{Determine whether } (-x)^2 - (-x) + 8 \text{ is equivalent to } x^2 - x + 8. \][/tex]
Thus, the correct statement is:
[tex]\[ \text{Determine whether } (-x)^2 - (-x) + 8 \text{ is equivalent to } x^2 - x + 8. \][/tex]
