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.