The given expression for the difference quotient is:

$\frac{(2+h)^2 - 2^2}{h}$

This matches the general form of the difference quotient:

$\frac{f(a+h) - f(a)}{h}$

To identify $f(x)$ and $a$, we can compare terms.

1. The term $(2+h)^2$ corresponds to $f(a+h)$, which suggests that $f(x) = x^2$ (since $(a+h)^2$ implies a quadratic function).
2. The value of $a$ must be 2, as indicated by the expression $2^2$ in the difference quotient.

Thus, we have:

• $f(x) = x^2$
• $a = 2$

Would you like further explanation on how this conclusion was reached or more details about the difference quotient?

Here are 5 questions to deepen your understanding:

1. How would the difference quotient change for a different function like $f(x) = x^3$?
2. What is the geometric meaning of the difference quotient?
3. How does the difference quotient relate to the derivative?
4. Can you compute the difference quotient for $f(x) = x^2$ at $a = 3$?
5. What is the next step after finding the difference quotient in calculus?

Tip: The difference quotient is the foundation for calculating the derivative of a function!