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The problem asks for an equation based on the graph of \( y = \sqrt{x} \), which undergoes two transformations:

1. **Reflection across the origin**: This implies a reflection over both the x-axis and y-axis, making the new function \( y = -\sqrt{-x} \).
   
2. **Shifted left by 6 units**: A horizontal shift to the left means we replace \( x \) with \( x + 6 \).

Combining these two transformations, the new equation becomes:

\[
y = -\sqrt{-(x + 6)}
\]

Would you like further clarification or details on these transformations?

Here are 5 questions to explore further:

1. What is the effect of reflecting a function across the y-axis vs the x-axis?
2. How would shifting the graph up or down affect the equation?
3. Can you apply this method to different types of functions, such as \( y = x^2 \)?
4. How do vertical stretches or compressions change the appearance of the graph?
5. What happens when you reflect and shift other types of square root functions, such as \( y = \sqrt{x + 2} \)?

**Tip**: To understand how a graph changes with reflections and shifts, it's useful to plot the original and transformed functions on a graphing calculator or tool for a visual comparison.

Write an equation for a function that has a graph with the given characteristics. The shape of y = √x that is first reflected across the origin, then shifted left 6 units.

Learn how to transform the graph of the square root function y = √x by reflecting it across the origin and shifting it left by 6 units. This problem covers key concepts of graph transformations, reflections, and horizontal shifts, suitable for students in Grades 9-11.

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