transformation of y= square root x minus 3

To transform the function \( y = \sqrt{x} - 3 \), let's break down the transformation steps:

### 1. **Starting Function:**
   - The basic function is \( y = \sqrt{x} \).
   - This function represents the square root of \( x \), which is a curve starting from the origin (0,0) and increasing slowly as \( x \) increases.

### 2. **Vertical Shift:**
   - The transformation \( y = \sqrt{x} - 3 \) indicates a vertical shift.
   - Specifically, subtracting 3 shifts the entire graph **downward** by 3 units.

### **Summary of Transformation:**
- The graph of \( y = \sqrt{x} \) is shifted down by 3 units to get the graph of \( y = \sqrt{x} - 3 \).

### **Resulting Graph:**
- The new graph still starts at \( x = 0 \), but the starting point is now at \( (0, -3) \).
- The curve follows the same shape as \( y = \sqrt{x} \) but is shifted downward.

Would you like more details or have any questions?

### Related Questions:
1. How would you transform \( y = \sqrt{x} + 2 \)?
2. What would the graph of \( y = \sqrt{x + 3} \) look like?
3. How does the function \( y = -\sqrt{x} \) differ from \( y = \sqrt{x} \)?
4. What are the domain and range of the function \( y = \sqrt{x} - 3 \)?
5. How do horizontal shifts affect the graph of \( y = \sqrt{x} \)?

### Tip:
Always check the domain of the original function before applying transformations to ensure the results are valid over the intended range.

Explore how to transform the function y = sqrt(x) - 3 with detailed steps and examples. Understand the vertical shift and its impact on the graph. Suitable for high school students studying functions and transformations.

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