Answered

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Instructions: Based on the information given in the problem, select the accurate transformation.

What is the effect on the graph of the function [tex]f(x) = 3 \cdot 3^x[/tex] when [tex]f(x)[/tex] is replaced with [tex]f(x) - 4[/tex]?

Select one:
A. Translate vertically 4 units up.
B. Translate horizontally 4 units left.
C. Translate horizontally 4 units left.
D. Translate vertically 4 units down.

Sagot :

GinnyAnswer
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.
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