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The question asks: "If point (4, 5) is on the graph of a function, which equation must be true?"

Given that the point \((4, 5)\) lies on the graph of a function, this means that when \(x = 4\), the output (or \(y\)-value) of the function is 5. In functional notation, this would be written as:

\[
f(4) = 5
\]

Now, let's examine the choices:

- \(f(5) = 4\) — Incorrect because it implies that when \(x = 5\), the output is 4.
- \(f(5,4) = 9\) — Incorrect because this notation doesn't apply to single-variable functions.
- **\(f(4) = 5\)** — This is correct because it reflects the point \((4, 5)\) on the function.
- \(f(5,4) = 1\) — Incorrect for the same reason as the earlier multi-variable notation.

The correct answer is:

\[
\boxed{f(4) = 5}
\]

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to explore further:
1. What does it mean for a point to lie on the graph of a function?
2. How do you interpret functional notation like \(f(x)\)?
3. Can a function have more than one output for the same input? Why or why not?
4. What is the difference between a single-variable and a multi-variable function?
5. How can we graphically verify if a point belongs to a function?

**Tip**: Always remember that \(f(x)\) refers to the value of the function when the input is \(x\).

If point (4, 5) is on the graph of a function, which equation must be true?

Explore how to identify the correct equation when a point lies on the graph of a function. This problem involves basic functional notation and graph interpretation, suitable for Grades 8-10.

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