A function f is given, and the indicated transformations are applied to its graph. Write the equation for the final transformed graph.
f(x) = 
3^square root of	x
;
shift 2 units to the right 

Given the function \( f(x) = 3^{\sqrt{x}} \), you are asked to apply a transformation to its graph by shifting it 2 units to the right.

### Step-by-step process:

1. **Original Function:** \( f(x) = 3^{\sqrt{x}} \)

2. **Horizontal Shift:** To shift a function 2 units to the right, replace \( x \) with \( x - 2 \) in the function. This shifts every point on the graph to the right by 2 units.

   - The new function after the transformation will be:
   \[
   f(x) = 3^{\sqrt{x - 2}}
   \]

Thus, the equation for the final transformed graph is:

\[
f(x) = 3^{\sqrt{x - 2}}
\]

Would you like more details on transformations or to clarify any of these steps? Here are some related questions:

1. How do you apply other types of transformations, such as vertical shifts or reflections?
2. What is the general form of a transformed function?
3. How would shifting the graph 2 units to the left affect the function?
4. What happens to the domain of the function after the shift?
5. How would this transformation affect the range of the function?

**Tip:** Horizontal shifts involve changing the \(x\) variable inside the function, while vertical shifts involve adding or subtracting a constant outside the function.

A function f is given, and the indicated transformations are applied to its graph. Write the equation for the final transformed graph.
f(x) = 3^√x;
shift 2 units to the right.

Understand how to apply a horizontal shift to the function f(x) = 3^√x. This example demonstrates shifting the graph two units to the right, following key transformation rules. Suitable for high school students in Grades 9-12.

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