The graph of f(x)=(square root of x) is given below. Write the equation of a function h(x) which would first shift the graph down 6 units then reflect it over the x-axis

To find the equation of the function \( h(x) \) that transforms the graph of \( f(x) = \sqrt{x} \), we need to apply two transformations:

1. **Shift down by 6 units**: This transformation subtracts 6 from the original function. So the new function becomes:
   \[
   f(x) - 6 = \sqrt{x} - 6
   \]

2. **Reflect over the x-axis**: Reflecting a function over the x-axis involves multiplying the entire function by \(-1\). Applying this to the function from step 1:
   \[
   h(x) = -(\sqrt{x} - 6)
   \]
   This simplifies to:
   \[
   h(x) = -\sqrt{x} + 6
   \]

Thus, the equation of the function \( h(x) \) is:
\[
h(x) = -\sqrt{x} + 6
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you reflect a graph over the y-axis?
2. What happens to a graph when you shift it left or right?
3. What are vertical and horizontal stretches and compressions?
4. How do you shift a graph up or down?
5. How do multiple transformations (e.g., shifts and reflections) interact with each other?

**Tip**: When applying multiple transformations to a function, always perform vertical shifts last.

The graph of f(x) = (square root of x) is given below. Write the equation of a function h(x) which would first shift the graph down 6 units then reflect it over the x-axis.

Learn how to transform the graph of f(x) = √x by shifting it down 6 units and reflecting it over the x-axis. This detailed explanation breaks down key concepts such as function shifting and reflection, suitable for students in Grades 9-11.

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