Given that $f(x) = 4x + 3$, to evaluate $f(x+h)$, we substitute $x+h$ into the function $f(x)$.

$f(x+h) = 4(x+h) + 3$

Now, simplify the expression:

$f(x+h) = 4x + 4h + 3$

Thus, $f(x+h) = 4x + 4h + 3$.

Would you like further details on function evaluation or how this relates to limits and derivatives?

Here are 5 related questions to expand on this concept:

1. What is the difference between evaluating $f(x+h)$ and $f(h)$?
2. How do you find the difference quotient $\frac{f(x+h) - f(x)}{h}$?
3. What is the geometric interpretation of $f(x+h)$ for a linear function?
4. How would the expression change if $f(x)$ were a quadratic function?
5. Can you apply this to find the derivative of $f(x)$?

Tip: When evaluating functions with variables like $x+h$, always distribute carefully and watch out for any simplifications.