To understand how the graph of the function [tex]\( f(x) = 3(3^x) \)[/tex] is affected when [tex]\( f(x) \)[/tex] is replaced with [tex]\( f(x) - 4 \)[/tex], we need to analyze the transformation applied.
1. Original Function:
- [tex]\( f(x) = 3(3^x) \)[/tex]
2. Transformed Function:
- [tex]\( f(x) - 4 \)[/tex]
### Understanding the Transformation
- Vertical Shifts: Adjusting the function by adding or subtracting a constant affects the graph vertically.
- [tex]\( f(x) + c \)[/tex]: Translates the graph [tex]\( c \)[/tex] units up.
- [tex]\( f(x) - c \)[/tex]: Translates the graph [tex]\( c \)[/tex] units down.
- Horizontal Shifts: Adjusting the function by adding or subtracting a constant within the argument of the function affects the graph horizontally.
- [tex]\( f(x + c) \)[/tex]: Translates the graph [tex]\( c \)[/tex] units left.
- [tex]\( f(x - c) \)[/tex]: Translates the graph [tex]\( c \)[/tex] units right.
In this specific instance:
- The transformation applied is [tex]\( f(x) - 4 \)[/tex].
- This means we are subtracting 4 from the entire function value, which translates the graph vertically.
### Conclusion:
- The correct transformation is a vertical shift.
- Specifically, the graph of the function is translated 4 units down.
### Answer:
Translate vertically 4 units down.
