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]
