To determine the validity of each statement regarding the function [tex]\( f(x) \)[/tex] defined by the set of ordered pairs [tex]\( \{(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)\} \)[/tex], we will check each statement one by one.
Statement 1: [tex]\( f(-3) = 8 \)[/tex]
First, we check if the point [tex]\((-3, 8)\)[/tex] is included in the set of ordered pairs for [tex]\( f(x) \)[/tex]:
- Our set of ordered pairs is [tex]\( \{(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)\} \)[/tex].
- There is no ordered pair [tex]\((-3, 8)\)[/tex] in the provided function.
Therefore, [tex]\( f(-3) = 8 \)[/tex] is False.
Statement 2: [tex]\( f(3) = 5 \)[/tex]
Next, we check if the point [tex]\((3, 5)\)[/tex] is included in the set of ordered pairs for [tex]\( f(x) \)[/tex]:
- Our set of ordered pairs is still [tex]\( \{(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)\} \)[/tex].
- There is no ordered pair [tex]\((3, 5)\)[/tex] in the provided function.
Thus, [tex]\( f(3) = 5 \)[/tex] is False.
Statement 3: [tex]\( f(8) = 0 \)[/tex]
Now, we check the value of [tex]\( f(8) \)[/tex] from the set of ordered pairs:
- From the pair [tex]\((8, -3)\)[/tex], we see that when [tex]\( x = 8 \)[/tex], then [tex]\( f(8) = -3 \)[/tex].
Therefore, [tex]\( f(8) = 0 \)[/tex] is False.
Statement 4: [tex]\( f(-6) = 10 \)[/tex]
Finally, we check the value of [tex]\( f(-6) \)[/tex] from the set of ordered pairs:
- From the pair [tex]\((-6, 10)\)[/tex], we find that when [tex]\( x = -6 \)[/tex], then [tex]\( f(-6) = 10 \)[/tex].
Thus, [tex]\( f(-6) = 10 \)[/tex] is True.
In conclusion, the validity of each statement is:
- [tex]\( f(-3) = 8 \)[/tex] — False
- [tex]\( f(3) = 5 \)[/tex] — False
- [tex]\( f(8) = 0 \)[/tex] — False
- [tex]\( f(-6) = 10 \)[/tex] — True
Hence, the correct evaluation of the given statements yields the result: [tex]\( \boxed{(False, False, False, True)} \)[/tex].
