To determine which equation must be true regarding the function based on the given point [tex]\((-3, -5)\)[/tex], follow these steps:
1. Understand the Concept:
- The point [tex]\((-3, -5)\)[/tex] on the graph of a function means that when the input (or [tex]\(x\)[/tex]-value) is [tex]\(-3\)[/tex], the corresponding output (or [tex]\(y\)[/tex]-value) is [tex]\(-5\)[/tex].
- This can be interpreted directly as the function notation [tex]\(f(-3) = -5\)[/tex], meaning the function [tex]\(f\)[/tex] takes the input [tex]\(-3\)[/tex] and maps it to [tex]\(-5\)[/tex].
2. Analyze the Given Choices:
- Option 1: [tex]\(f(-3) = -5\)[/tex]:
- This option directly states that when the input to the function is [tex]\(-3\)[/tex], the output is [tex]\(-5\)[/tex], which matches our understanding.
- Option 2: [tex]\(f(-3, -5) = -8\)[/tex]:
- This suggests that the function [tex]\(f\)[/tex] takes two inputs [tex]\(-3\)[/tex] and [tex]\(-5\)[/tex]. However, our original information tells us that [tex]\(-3\)[/tex] is the input and [tex]\(-5\)[/tex] is the output for a function that likely has a single input.
- Option 3: [tex]\(f(-5) = -3\)[/tex]:
- This implies that when the input is [tex]\(-5\)[/tex], the output is [tex]\(-3\)[/tex]. This does not align with the given point [tex]\((-3, -5)\)[/tex] since it reverses the roles.
- Option 4: [tex]\(f(-5, -3) = -2\)[/tex]:
- Similar to Option 2, this suggests a function that takes two inputs, which doesn't match the context provided by the point on a function graph.
3. Conclusion:
- The true statement about the function given the point [tex]\((-3, -5)\)[/tex] is:
[tex]\[
f(-3) = -5
\][/tex]
Therefore, the correct equation must be:
[tex]\[
f(-3) = -5
\][/tex]
