To transform the function $f(x) = x^2$ according to the given instructions, we need to apply the following steps:

Step 1: Shift the graph to the right 4 units

To shift the graph of a function to the right by 4 units, we replace $x$ with $x - 4$. This gives us:

$f(x) = (x - 4)^2$

Step 2: Stretch the graph horizontally by a factor of 4

To stretch the graph horizontally by a factor of 4, we divide the $x$-term inside the parentheses by 4. This changes the equation to:

$h(x) = \left( \frac{x - 4}{4} \right)^2$

Final Equation:

Thus, the equation of the transformed function $h(x)$ is:

$h(x) = \left( \frac{x - 4}{4} \right)^2$

Would you like more details on how these transformations work? Or do you have any other questions?

Related questions:

1. How would the graph change if we shifted it left instead of right?
2. What effect does a vertical stretch or shrink have on the graph of a function?
3. How do horizontal transformations affect the graph differently than vertical ones?
4. What is the general form of a quadratic function after a horizontal shift and stretch?
5. How do you combine multiple transformations (e.g., shift and stretch) into one function?

Tip: To stretch or compress horizontally, divide the $x$-terms inside the function by the factor you want to stretch by.