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

Shift to the left 3 units and shift up 12 units

Answer 1

To transform the function \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we can break this down into two steps:

1. **Horizontal Shift**: Change \( x^2 \) to \( f(x - 3) \). This represents a shift to the right by 3 units.

2. **Vertical Shift**: Then, taking \( f(x - 3) \) and transforming it to \( f(x - 3) + 12 \) means shifting the graph up by 12 units.

Therefore, the complete transformation consists of first shifting to the right 3 units, and then shifting up 12 units.

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