Transform the solid black function to match the dotted function.
y= square root of x

To transform the solid black function \( y = \sqrt{x} \) to match the dotted function, you need to apply specific transformations such as translations, reflections, stretches, or compressions. 

The general form of the transformation for a function \( f(x) = \sqrt{x} \) can be written as:

\[
y = a \sqrt{b(x - h)} + k
\]

Where:
- \( a \) is a vertical stretch/compression or reflection.
- \( b \) is a horizontal stretch/compression.
- \( h \) is a horizontal shift (left or right).
- \( k \) is a vertical shift (up or down).

To identify the transformations needed, you would compare the key points and shape of the solid function to the dotted function.

Would you like to provide more details about the transformations you observe, or do you have any questions?

Here are 5 questions related to the transformation:

1. Does the dotted function appear to be shifted horizontally or vertically from the original function?
2. Is the dotted function reflected across the x-axis or y-axis?
3. Is the dotted function stretched or compressed compared to the original function?
4. Does the dotted function have any vertical or horizontal shifts?
5. Are the points of intersection with the axes the same for both functions?

**Tip:** When transforming functions, always start by identifying any shifts (horizontal or vertical) before considering stretches, compressions, or reflections.

Learn how to transform the solid black function y = sqrt(x) to match the dotted function. Understand the necessary translations, reflections, stretches, or compressions involved in transforming functions. Ideal for high school students studying function transformations.

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