https://file.aiquickdraw.com/mathbot/file/1726794034482b7lovdpa.jpg

The equation in the image is:

\[
f(a+h) = 4(a+h)^3
\]

This represents a function \( f \) evaluated at \( a+h \), where the output is four times the cube of \( a+h \).

Would you like me to expand this expression, differentiate it, or do something else with it?

Here are a few related questions you could consider:
1. What is the expanded form of \( 4(a+h)^3 \)?
2. How do you find the derivative of \( f(a+h) \) with respect to \( h \)?
3. What is the significance of cubic functions in calculus?
4. How does shifting a function by \( h \) affect its behavior?
5. Can this function model any physical phenomena like volume or growth?

**Tip**: When dealing with functions involving both variables and constants, expanding them can reveal useful insights for differentiation and integration.

What is the function represented by f(a+h) = 4(a+h)^3?

Explore the function f(a+h) = 4(a+h)^3. This problem involves cubic functions and their applications. Discover how to expand, differentiate, and analyze cubic expressions. Suitable for Grades 9-12.

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