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.

Learn how to evaluate f(x+h) when f(x) = 4x + 3 with a step-by-step solution. This problem covers essential algebraic concepts including function evaluation, the distributive property, and simplifying expressions. Ideal for students in Grades 8-10.

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