Describe the transformation of the graph of the parent function y = √x for the function y = √x + 7 + 5.

The graph is shifted 7 units 
 and 5 units 
.

The transformation of the graph of the parent function \( y = \sqrt{x} \) for the function \( y = \sqrt{x} + 7 + 5 \) involves vertical and horizontal shifts. Let’s break down the transformation step by step:

The given function is:

\[
y = \sqrt{x} + 7 + 5
\]

This can be rewritten as:

\[
y = (\sqrt{x}) + 7 + 5 = \sqrt{x} + 12
\]

### Analysis of the Transformation

1. **Vertical Shift:** The term \( +12 \) indicates a vertical shift. The graph of the parent function \( y = \sqrt{x} \) is shifted **12 units up**. This is because adding a constant outside the square root function affects the vertical position of the graph.

2. **Horizontal Shift:** There is no horizontal shift in this case because there is no transformation inside the square root (no addition or subtraction affecting the \( x \) term directly).

### Final Description
The graph of \( y = \sqrt{x} \) is shifted **12 units up**.

If you originally saw the phrase "shifted 7 units" and "5 units" in your question, it may have been referring to an error. The correct transformation for this function is **12 units up** and no horizontal shift.

Would you like to explore this further or check another problem?

### Related Questions:
1. What would be the transformation if the function were \( y = \sqrt{x - 3} + 7 \)?
2. How would the graph shift if the function were \( y = -\sqrt{x} + 4 \)?
3. If the function were \( y = 2\sqrt{x} - 5 \), what would the transformations be?
4. How does a horizontal shift differ from a vertical shift in terms of function notation?
5. What would the domain and range of \( y = \sqrt{x} + 12 \) be?

### Tip:
Always check if a transformation is applied inside or outside the function

Describe the transformation of the graph of the parent function y = √x for the function y = √x + 7 + 5.

Explore the transformation of the graph of y = √x for the function y = √x + 7 + 5. Learn how vertical and horizontal shifts apply to square root functions with this detailed solution. Suitable for students in Grades 9-10.

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