Question
f(x) to f(x - 5) +4 translated ____ units to the ___ and ___ units __
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GPT-4o mini
The transformation from \( f(x) \) to \( f(x - 5) + 4 \) involves two changes:
1. **Horizontal Translation**: The term \( f(x - 5) \) indicates a horizontal translation. Specifically, it translates the graph of the function to the right by 5 units. This is because subtracting within the function's argument (\( x - 5 \)) moves the graph to the right.
2. **Vertical Translation**: The term \( + 4 \) indicates a vertical translation. This shifts the graph of the function upward by 4 units.
So, to fill in the blanks:
The function \( f(x) \) translated **5** units to the **right** and **4** units **upward**.
1. **Horizontal Translation**: The term \( f(x - 5) \) indicates a horizontal translation. Specifically, it translates the graph of the function to the right by 5 units. This is because subtracting within the function's argument (\( x - 5 \)) moves the graph to the right.
2. **Vertical Translation**: The term \( + 4 \) indicates a vertical translation. This shifts the graph of the function upward by 4 units.
So, to fill in the blanks:
The function \( f(x) \) translated **5** units to the **right** and **4** units **upward**.
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