Question

What is the order of combinations to transform f(x)=x2
to f(x−3)+12
?(1 point)
Responses

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 left 3 units and shift down 12 units.
Shift to the left 3 units and shift down 12 units.

Shift to the right 3 units and shift up 12 units.
Shift to the right 3 units and shift up 12 units.

Shift to the left 3 units and shift up 12 units.

Answer 1

To transform \( f(x) = x^2 \) to \( f(x-3) + 12 \), we will break down the transformations step by step.

1. **Transform \( f(x) = x^2 \) to \( f(x-3) \)**:
- The expression \( f(x-3) \) represents a horizontal shift to the **right** by 3 units. So, the first transformation is a shift to the right by 3 units.

2. **Transform \( f(x-3) \) to \( f(x-3) + 12 \)**:
- The expression \( f(x-3) + 12 \) represents a vertical shift **up** by 12 units. So, the second transformation is a shift up by 12 units.

Putting it all together, the order of transformations is:
**Shift to the right 3 units and shift up 12 units.**

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