The function [tex]\( f(x) \)[/tex] is given by the set of ordered pairs:

[tex]\[ \{(8,-3), (0,4), (1,-5), (2,-1), (-6,10)\} \][/tex]

Which is true regarding the function?

A. [tex]\( f(-3) = 8 \)[/tex]

B. [tex]\( f(3) = 5 \)[/tex]

C. [tex]\( f(8) = 0 \)[/tex]

D. [tex]\( f(-6) = 10 \)[/tex]



Answer :

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].