If the point $(7, 8)$ lies on the graph of a function $f$, this means that when $x = 7$, the corresponding $y$-value is $8$. In other words, the function evaluated at $7$ gives $8$, or:

$f(7) = 8$

Thus, the correct answer is:

$f(7) = 8$

Would you like any further details or clarification? Here are five related questions:

1. What does it mean for a point to lie on the graph of a function?
2. How can you determine if a given point satisfies a function?
3. What is the general relationship between points on a graph and function evaluations?
4. What other types of questions can involve function evaluation like this?
5. How do you find the equation of a function given multiple points on its graph?

Tip: Remember, the notation $f(x)$ always refers to the $y$-value (or output) corresponding to the input $x$.