https://file.aiquickdraw.com/mathbot/file/172550514046436deai32.jpg

The image displays the function \( f(x) = 2x - 2 \), and you have requested to compute \( f(a+h) \).

To calculate \( f(a+h) \), substitute \( a+h \) in place of \( x \) in the function \( f(x) \).

\[
f(a+h) = 2(a+h) - 2
\]

Now, distribute the 2:

\[
f(a+h) = 2a + 2h - 2
\]

Thus, the expression for \( f(a+h) \) is:

\[
f(a+h) = 2a + 2h - 2
\]

Would you like further details or explanations?

Here are some related questions to explore:

1. What is \( f(a+h) - f(a) \) for the function \( f(x) = 2x - 2 \)?
2. How do you interpret the difference quotient \( \frac{f(a+h) - f(a)}{h} \)?
3. What is the derivative of \( f(x) = 2x - 2 \)?
4. How would you graph the function \( f(x) = 2x - 2 \)?
5. What is the slope of the function \( f(x) = 2x - 2 \)?

**Tip:** The expression \( f(a+h) \) is a key step in finding the derivative using the definition.

Learn how to compute f(a+h) for the linear function f(x) = 2x - 2 by substituting and simplifying. Explore key algebraic concepts like linear functions and substitution. Suitable for high school students in Grades 9-12.

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