Question

What is the order of combinations to transform f(x)=x^2 to f(x−3)+12 ?(1 point) Responses Shift to the left 3 units and shift down 12 units. Shift to the left 3 units and shift down 12 units. Shift to the left 3 units and shift up 12 units. Shift to the left 3 units and shift up 12 units. Shift to the right 3 units and shift down 12 units. Shift to the right 3 units and shift down 12 units. Shift to the right 3 units and shift up 12 units.

Answer 1

To transform the function \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we need to analyze the transformations involved.

1. **Transforming \( f(x) \) to \( f(x - 3) \)**: This part of the transformation indicates a horizontal shift. When \( x \) is replaced by \( x - 3 \), the graph shifts **to the right** by 3 units.

2. **Transforming \( f(x - 3) \) to \( f(x - 3) + 12 \)**: This part adds 12 to the function, which results in a vertical shift. When you add a positive number to the function, it shifts **upward**. Thus, adding 12 shifts the graph **up** by 12 units.

Putting it all together, the order of transformations is:
- Shift to the right 3 units (due to \( x - 3 \))
- Shift up 12 units (due to the addition of 12)

So, the correct response is:
**Shift to the right 3 units and shift up 12 units.**