The given function is:

\[
f(x + h) = 3(x + h) - 9
\]

Now let's simplify the expression:

\[
f(x + h) = 3x + 3h - 9
\]

Thus, the simplified form of \( f(x + h) \) is:

\[
f(x + h) = 3x + 3h - 9
\]

Would you like any further details or have any specific questions about this?

Here are 5 related questions to further your understanding:

1. What is the original function \( f(x) \) based on the given \( f(x + h) \)?
2. How would you find \( f'(x) \), the derivative of \( f(x) \), using the definition of the derivative?
3. Can you calculate \( f(2 + h) \) from the simplified expression?
4. How would you expand and simplify \( f(x + h) \) if the original function was quadratic, e.g., \( f(x) = x^2 \)?
5. What happens to the expression if \( h = 0 \)? What does this tell you about \( f(x + 0) \)?

**Tip:** When working with function shifts like \( f(x + h) \), always simplify the expression first to see how the shift affects the function.

Understand how to simplify f(x + h) = 3(x + h) - 9 and explore function shifts with this algebraic example. Learn how to break down the expression and simplify it for easier understanding. Suitable for students in Grades 8-10.

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