Transform the solid black function to match the dotted function. y= square root of x. f(x+__ )+__

To transform the solid black function \( y = \sqrt{x} \) to match the dotted function using the form \( f(x + h) + k \), you need to determine the horizontal shift \( h \) and vertical shift \( k \).

The transformation is:

\[
y = \sqrt{x + h} + k
\]

Where:
- \( h \) represents the horizontal shift (left or right).
- \( k \) represents the vertical shift (up or down).

### Steps to find \( h \) and \( k \):
1. **Horizontal Shift (\( h \))**: 
   - If the dotted function is shifted to the left of the solid black function, \( h \) will be positive.
   - If the dotted function is shifted to the right, \( h \) will be negative.

2. **Vertical Shift (\( k \))**: 
   - If the dotted function is shifted upwards from the solid black function, \( k \) will be positive.
   - If the dotted function is shifted downwards, \( k \) will be negative.

So, the transformed function will be:

\[
y = \sqrt{x + h} + k
\]

To give you the exact values of \( h \) and \( k \), I'd need information about the dotted function's shifts from the original function \( y = \sqrt{x} \).

Do you have any specific values or points on the dotted function that indicate these shifts? 

Here are 5 questions that could help clarify the transformation:

1. What is the x-coordinate of the vertex of the dotted function compared to the original?
2. What is the y-coordinate of the vertex of the dotted function compared to the original?
3. Does the dotted function intersect the y-axis at a different point than the original function?
4. Is there any noticeable compression or stretching of the dotted function?
5. Are the endpoints of the dotted function different from those of the original function?

**Tip:** You can often find the value of \( h \) by determining where the graph intersects the x-axis and the value of \( k \) by checking where it intersects the y-axis.

Learn how to transform the square root function y = sqrt(x) to match another function using the transformation form f(x + h) + k. Understand the steps involved in determining the horizontal and vertical shifts for the transformation.

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