Let's examine each equation one by one using the given set of ordered pairs for the function [tex]\( f \)[/tex].
The function [tex]\( f \)[/tex] is defined by the following pairs:
[tex]\[
\{ (1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1) \}
\][/tex]
To verify each equation, we will look at the defined pairs to see if they match.
1. [tex]\( f(-10) = 1 \)[/tex]:
- According to the ordered pairs, [tex]\( f(-10) = 2 \)[/tex]. Thus, this equation is not true.
2. [tex]\( f(2) = -10 \)[/tex]:
- The function [tex]\( f \)[/tex] does not include a pair with [tex]\( 2 \)[/tex] as the input. So [tex]\( f(2) \)[/tex] is not defined in this context, making this equation not true.
3. [tex]\( f(0) = 6 \)[/tex]:
- According to the ordered pairs, [tex]\( f(0) = 6 \)[/tex]. Thus, this equation is true.
4. [tex]\( f(1) = -10 \)[/tex]:
- According to the ordered pairs, [tex]\( f(1) = 0 \)[/tex]. Thus, this equation is not true.
After reviewing all the provided equations, the only equation that is true is:
[tex]\[ f(0) = 6 \][/tex]
So the correct equation is:
[tex]\[ f(0) = 6 \][/tex]
