Kiara performs a vertical stretch of the square root parent function. Which graph depicts this transformation?

A vertical stretch of a function occurs when the output values (y-values) are multiplied by a factor greater than 1. The square root parent function is given by:

\[
f(x) = \sqrt{x}
\]

When Kiara performs a vertical stretch, the function becomes:

\[
g(x) = a \sqrt{x}
\]

where \( a > 1 \) is the vertical stretch factor.

### Effects of the Transformation:
- The graph of \( g(x) = a\sqrt{x} \) will stretch vertically, meaning it will appear taller or "stretched" compared to the parent function \( f(x) = \sqrt{x} \).
- The graph will still pass through the origin (0, 0) because \( \sqrt{0} = 0 \), and the shape of the curve will remain the same but with larger values for \( y \).

In summary, the graph depicting this transformation will look similar to the square root parent function, but the curve will rise more steeply.

### Do you have a specific graph to compare? Or do you want more details on graph transformations?

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Here are five related questions for further exploration:
1. How would the graph look if Kiara applied a vertical compression instead of a stretch?
2. What happens to the domain and range after the vertical stretch?
3. Can a vertical stretch affect the x-intercepts of a function?
4. How would horizontal transformations affect the square root function?
5. What is the effect of a negative vertical stretch on the graph?

**Tip:** Vertical stretches and compressions only affect the y-values; they do not change the x-values of the function.

Discover how to apply a vertical stretch to the square root function. Learn the mathematical transformation involved, how the graph changes, and see examples. Ideal for students in Grades 9-11 studying function transformations.

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