Question
f(x)to f(x+2)+1 it is translated ____ units to the _____ and _____ units ___
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GPT-4o mini
The translation of the function \( f(x) \) to \( f(x+2) + 1 \) involves two transformations:
1. **Horizontal translation:** The \( f(x+2) \) part indicates a horizontal shift of 2 units to the **left**. This is because replacing \( x \) with \( x + c \) translates the function \( c \) units in the opposite direction.
2. **Vertical translation:** The \( +1 \) indicates a vertical shift of 1 unit **up**. This means that the entire function is raised by 1 unit.
Putting it all together, the transformation can be described as:
- It is translated **2 units to the left** and **1 unit up**.
1. **Horizontal translation:** The \( f(x+2) \) part indicates a horizontal shift of 2 units to the **left**. This is because replacing \( x \) with \( x + c \) translates the function \( c \) units in the opposite direction.
2. **Vertical translation:** The \( +1 \) indicates a vertical shift of 1 unit **up**. This means that the entire function is raised by 1 unit.
Putting it all together, the transformation can be described as:
- It is translated **2 units to the left** and **1 unit up**.
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