The point [tex]\((-3,-5)\)[/tex] is on the graph of a function. Which equation must be true regarding the function?

A. [tex]\(f(-3) = -5\)[/tex]
B. [tex]\(f(-3,-5) = -8\)[/tex]
C. [tex]\(f(-5) = -3\)[/tex]
D. [tex]\(f(-5,-3) = -2\)[/tex]



Answer :

To determine which equation must be true given that the point [tex]\((-3,-5)\)[/tex] is on the graph of a function, let's analyze the implications of each statement.

1. Statement: [tex]\(f(-3) = -5\)[/tex]

If the point [tex]\((-3, -5)\)[/tex] is on the graph of the function [tex]\(f\)[/tex], it means that when the function is evaluated at [tex]\(x = -3\)[/tex], the output (or [tex]\(y\)[/tex]-value) is [tex]\(-5\)[/tex]. Mathematically, this is written as [tex]\(f(-3) = -5\)[/tex].

2. Statement: [tex]\(f(-3, -5) = -8\)[/tex]

This statement implies a function of two variables, where [tex]\(f\)[/tex] takes two arguments. The point [tex]\((-3, -5)\)[/tex] as given in the problem is not implied to be a pair of input values but rather a [tex]\(x\)[/tex]-value of [tex]\(-3\)[/tex] giving an output of [tex]\(-5\)[/tex].

3. Statement: [tex]\(f(-5) = -3\)[/tex]

This equation is suggesting that the function evaluated at [tex]\(x = -5\)[/tex] results in [tex]\(-3\)[/tex], which does not correspond to the given point [tex]\((-3, -5)\)[/tex].

4. Statement: [tex]\(f(-5, -3) = -2\)[/tex]

Similar to the second statement, this suggests a function of two variables, which is not indicated by the problem. The point [tex]\((-3, -5)\)[/tex] does not provide [tex]\(-5\)[/tex] and [tex]\(-3\)[/tex] as input values for the function.

Given all the choices, the only equation that correctly reflects the information that the point [tex]\((-3, -5)\)[/tex] is on the graph of the function is:

[tex]\[ f(-3) = -5 \][/tex]

Therefore, the true statement regarding the function is:

[tex]\[ f(-3) = -5 \][/tex]