Let's consider the point [tex]\((-3, -5)\)[/tex] on the graph of the function. This point informs us about the behavior of the function at [tex]\( x = -3 \)[/tex]. The notation [tex]\( (-3, -5) \)[/tex] means that when [tex]\( x = -3 \)[/tex], the function [tex]\( f \)[/tex] maps [tex]\( x \)[/tex] to [tex]\( y = -5 \)[/tex]. Hence, this indicates that [tex]\( f(-3) = -5 \)[/tex].
Now let's analyze each given equation to determine which one is true:
1. [tex]\( f(-3) = -5 \)[/tex]:
- This is our candidate, as it directly states the behavior we've identified: when [tex]\( x = -3 \)[/tex], the function outputs [tex]\( -5 \)[/tex].
2. [tex]\( f(-3, -5) = -8 \)[/tex]:
- This form is not typically used for functions that map a single [tex]\( x \)[/tex] to a single [tex]\( y \)[/tex]. This notation suggests a function of two variables, which is not the case here.
3. [tex]\( f(-5) = -3 \)[/tex]:
- This would imply that when [tex]\( x = -5 \)[/tex], the function outputs [tex]\( -3 \)[/tex]. However, our given information only tells us about the point [tex]\((-3, -5)\)[/tex], not about [tex]\( f(-5) \)[/tex].
4. [tex]\( f(-5, -3) = -2 \)[/tex]:
- Similar to the second option, this suggests a function of two variables. Additionally, the values [tex]\((-5, -3)\)[/tex] are not relevant to our given point.
Thus, the only equation that must be true considering the point [tex]\((-3, -5)\)[/tex] is:
[tex]\[ f(-3) = -5 \][/tex]
So, the correct choice is the first one.
