Let f(x) = 4Vx
If g(x) is the graph of f(x) shifted up 3 units and right 3 units, write a formula for g(x)

To find the formula for \( g(x) \), the function \( f(x) = 4\sqrt{x} \) needs to be shifted up 3 units and to the right 3 units.

### Step-by-step process:

1. **Shift right by 3 units**:  
   To shift a function horizontally to the right by 3 units, replace \( x \) with \( x - 3 \) in the function.  
   So, shifting \( f(x) = 4\sqrt{x} \) to the right by 3 units gives:  
   \[
   f(x - 3) = 4\sqrt{x - 3}
   \]

2. **Shift up by 3 units**:  
   To shift a function vertically up by 3 units, add 3 to the entire function.  
   So, shifting \( 4\sqrt{x - 3} \) up by 3 units gives:  
   \[
   g(x) = 4\sqrt{x - 3} + 3
   \]

Thus, the formula for \( g(x) \) is:
\[
g(x) = 4\sqrt{x - 3} + 3
\]

Would you like further details or have any questions?

### Related Questions:
1. What is the graph of \( f(x) = 4\sqrt{x} \) before any shifts?
2. How does shifting a function horizontally or vertically affect its domain and range?
3. What is the domain of \( g(x) = 4\sqrt{x - 3} + 3 \)?
4. How would the graph change if we shifted \( f(x) \) left by 3 units instead?
5. How do we determine the inverse of the function \( f(x) \)?

**Tip:** Always check the domain of a function after performing transformations, as shifts can alter where the function is defined.

Let f(x) = 4√x. If g(x) is the graph of f(x) shifted up 3 units and right 3 units, write a formula for g(x).

Learn how to shift the square root function f(x) = 4√x both horizontally to the right by 3 units and vertically up by 3 units. This problem covers function transformations, square root functions, and their domains. Suitable for students in Grades 9-12.

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