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The problem asks to apply a transformation to the function \( f(x) = x^2 + 4 \) by shifting it:

- **3 units up**.
- **7 units to the right**.

Let's break down the transformations:

### 1. Shifting 3 units up:
When you move a function \( f(x) \) upward by \( k \) units, the transformation becomes:
\[
f(x) \to f(x) + k
\]
In this case, moving 3 units up:
\[
f(x) = x^2 + 4 \quad \text{becomes} \quad f(x) = x^2 + 4 + 3 = x^2 + 7
\]

### 2. Shifting 7 units to the right:
To shift a function to the right by \( h \) units, the transformation is:
\[
f(x) \to f(x - h)
\]
Here, moving 7 units to the right means:
\[
f(x) = (x - 7)^2 + 7
\]

### Final Transformed Function:
After applying both transformations, the final function is:
\[
f(x) = (x - 7)^2 + 7
\]

Now, I will graph the original function \( f(x) = x^2 + 4 \) and the transformed function \( f(x) = (x - 7)^2 + 7 \).It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still help you manually analyze the problem if you'd like, or I can attempt the graph again later.

Let me know if you would like further explanation on the steps we went through.

### 5 Related Questions:
1. What happens when you shift a quadratic function to the left instead of the right?
2. How would you apply a reflection along the x-axis to the function?
3. How does moving a graph up or down affect its vertex?
4. What changes occur in the graph if you multiply the quadratic function by a constant factor?
5. How do you find the vertex of a transformed quadratic function?

### Tip:
When graphing functions, always identify key points like the vertex or intercepts to better understand how transformations affect the function.

Desplazar la siguiente función: f(x) = x^2 + 4, - 3 unidades hacia arriba y 7 unidades a la derecha.

Learn how to transform the quadratic function f(x) = x^2 + 4 by shifting it 3 units up and 7 units to the right. This tutorial covers graph transformations for students in Grades 9-12, using vertical and horizontal shift formulas.

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