Graph the equation shown below by transforming the given graph of the parent function.
y, equals, 4, square root of, x, plus, 3, end square root
y=4
x+3
​

x
y
x
y
Answer
Attempt 1 out of 2

It seems like you're asking for the graph of a transformed square root function. However, your input may have some formatting issues. I will interpret your equation based on standard transformations and write it as:

\[
y = 4\sqrt{x + 3}
\]

This is a transformed version of the parent function \(y = \sqrt{x}\).

### Steps for Graphing

1. **Start with the parent function \(y = \sqrt{x}\):**
   - The graph of \(y = \sqrt{x}\) starts at the origin \((0, 0)\) and increases slowly as \(x\) increases.

2. **Apply the horizontal shift:**  
   The \(+3\) inside the square root shifts the graph **to the left by 3 units**. So instead of starting at \((0, 0)\), the graph now starts at \((-3, 0)\).

3. **Apply the vertical stretch:**  
   The factor of 4 outside the square root stretches the graph vertically by a factor of 4. This means for each value of \(x\), the output \(y\)-value is multiplied by 4 compared to the parent function.

### Key Points:
- The graph starts at \((-3, 0)\).
- As \(x\) increases, the graph rises faster due to the vertical stretch of 4.

### Would you like me to graph this equation for you or provide further details? 

Here are five related questions:
1. What are the effects of horizontal and vertical shifts on any parent function?
2. How does a vertical stretch or compression affect the shape of a graph?
3. How do you find the domain and range of a transformed function?
4. Can you describe how to graph the inverse of \(y = \sqrt{x + 3}\)?
5. How would this transformation change if it were \(y = -4\sqrt{x + 3}\)?

**Tip:** Always pay attention to signs inside and outside of a function when transforming a graph—positive values stretch, and negative values reflect or shift!

Graph the equation shown below by transforming the given graph of the parent function.
y = 4√(x + 3)

Learn how to graph the transformed square root function y = 4√(x + 3). This step-by-step guide covers vertical stretching and horizontal shifting, showing how to modify the parent function y = √x. Suitable for students in Grades 9-11.

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