Let f(x)=2 square root of x. If g(x) is the graph of f(x) shifted down 4 units and right 2 units, write formula for g(x)

The function \( f(x) = 2\sqrt{x} \) is shifted down by 4 units and to the right by 2 units to create the new function \( g(x) \).

1. **Right Shift by 2 Units**: To shift a function \( f(x) \) to the right by 2 units, we replace \( x \) with \( x - 2 \). This gives us:
   \[
   f(x - 2) = 2\sqrt{x - 2}
   \]

2. **Downward Shift by 4 Units**: To shift a function down by 4 units, we subtract 4 from the function. Applying this to \( 2\sqrt{x - 2} \), we get:
   \[
   g(x) = 2\sqrt{x - 2} - 4
   \]

Thus, the formula for \( g(x) \) is:
\[
g(x) = 2\sqrt{x - 2} - 4
\]

Would you like more details or have any questions about this? Here are some related questions to consider:

1. What happens if we shift \( f(x) \) left or up instead?
2. How would the graph of \( g(x) \) look compared to \( f(x) \)?
3. Can the domain of \( g(x) \) be affected by these shifts?
4. How can we generalize the formula for shifting any function horizontally and vertically?
5. What effect would shifting \( f(x) \) left by 3 units and up by 5 units have?

**Tip**: When shifting graphs horizontally, always adjust the variable inside the function. When shifting vertically, adjust the function itself.

Let f(x)=2 square root of x. If g(x) is the graph of f(x) shifted down 4 units and right 2 units, write formula for g(x).

Explore how to transform the function f(x) = 2√x by shifting it down 4 units and right 2 units. This problem covers key concepts in algebra, including function transformations and radical functions. Suitable for students in Grades 9-11.

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