Start with the graph of ​g(x)equalsStartRoot x EndRoot. Then shift it   ​unit(s).



To start with the graph of \( g(x) = \sqrt{x} \), we need to apply the desired transformations based on the shift described. However, you haven't specified the number of units or direction of the shift. Let's consider two common types of shifts and their effects:

1. **Horizontal Shift:**
   - If you shift the graph by \( h \) units to the right, the transformation is \( g(x) = \sqrt{x - h} \).
   - If you shift the graph by \( h \) units to the left, the transformation is \( g(x) = \sqrt{x + h} \).

2. **Vertical Shift:**
   - If you shift the graph by \( k \) units upward, the transformation is \( g(x) = \sqrt{x} + k \).
   - If you shift the graph by \( k \) units downward, the transformation is \( g(x) = \sqrt{x} - k \).

Could you specify how many units you'd like to shift and whether the shift is horizontal or vertical? Once you confirm, I can provide a more specific transformation.

Would you like further details on transformations or examples?

Here are 5 related questions:
1. How does shifting \( g(x) = \sqrt{x} \) horizontally affect its domain?
2. What is the effect of a vertical shift on the range of \( g(x) = \sqrt{x} \)?
3. How would you reflect \( g(x) = \sqrt{x} \) across the y-axis?
4. How does scaling vertically change the shape of \( g(x) = \sqrt{x} \)?
5. What happens if you shift \( g(x) = \sqrt{x} \) left and down simultaneously?

**Tip:** When shifting graphs, remember that horizontal shifts affect the input (x-value), and vertical shifts affect the output (y-value).

Start with the graph of g(x) equals StartRoot x EndRoot. Then shift it unit(s).

Explore how to shift the square root function g(x) = √x horizontally and vertically. Learn the key graph transformations and their impact on the function's domain and range. Suitable for high school students in Grades 9-12.

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