Given the function $f(x) = \frac{4}{x}$, you are looking to evaluate the function at $x = a + h$.

Substituting $x = a + h$ into the function $f(x)$, we get:

$f(a+h) = \frac{4}{a+h}$

This is the expression for $f(a+h)$ when $f(x) = \frac{4}{x}$.

Would you like further details on how this relates to other concepts, such as the difference quotient?

Here are five related questions:

1. How would you compute the difference quotient $\frac{f(a+h) - f(a)}{h}$ for this function?
2. What does the expression $f(a+h)$ represent in the context of a function's rate of change?
3. How does the limit of $\frac{f(a+h) - f(a)}{h}$ as $h$ approaches 0 relate to the derivative of $f(x)$?
4. How would you interpret $f(a+h)$ geometrically on the graph of $f(x)$?
5. What is the significance of evaluating a function at $a + h$ in calculus?

Tip: Understanding the difference quotient is crucial, as it is the foundation for finding the derivative, which represents the rate of change of a function.