Transform the given function f(x) as described and write the resulting function as an equation. f(x)=√x

Reflect over the x-axis

Translate right 2 units

Translate down 3 units

To apply the transformations to the given function \( f(x) = \sqrt{x} \), follow these steps:

1. **Reflect over the x-axis:** Reflecting a function over the x-axis changes its sign. So, the function becomes:
   \[
   f(x) = -\sqrt{x}
   \]

2. **Translate right 2 units:** Shifting the function to the right by 2 units means replacing \( x \) with \( x - 2 \) in the function. This gives:
   \[
   f(x) = -\sqrt{x - 2}
   \]

3. **Translate down 3 units:** Translating down by 3 units means subtracting 3 from the function:
   \[
   f(x) = -\sqrt{x - 2} - 3
   \]

Thus, the resulting function after applying all the transformations is:
\[
f(x) = -\sqrt{x - 2} - 3
\]

Would you like more details on any of these transformations or have any questions?

Here are 5 related questions:
1. How do we reflect a function over the y-axis?
2. What happens if we translate a function to the left instead of to the right?
3. How do we shift a function upward or downward by a certain number of units?
4. How would the graph of \( f(x) = \sqrt{x} \) look after only reflecting over the x-axis?
5. What effect does a vertical stretch or compression have on the function?

**Tip:** When applying multiple transformations, always perform reflections before translations to maintain accuracy in your transformations.

Transform the given function f(x) as described and write the resulting function as an equation. f(x) = √x. Reflect over the x-axis. Translate right 2 units. Translate down 3 units.

Learn how to transform the square root function f(x) = √x by reflecting it over the x-axis, translating it 2 units right, and 3 units down. This step-by-step solution explains the key transformations involved, suitable for students in Grades 9-11.

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