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 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.
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.

Answer 1

To transform the function \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we need to analyze what's happening in each part of the transformation.

1. **Starting with \( f(x) = x^2 \)**:
- This is the original function.

2. **Transforming to \( f(x - 3) \)**:
- The expression \( f(x - 3) \) means we are replacing \( x \) with \( x - 3 \).
- This transformation shifts the graph **to the right by 3 units**.

3. **Adding 12**:
- The \( + 12 \) indicates a vertical shift.
- This shifts the graph **up by 12 units**.

Combining these two transformations, the order is:
- Shift **to the right 3 units** (first), and then
- Shift **up 12 units** (second).

Thus, the correct response is:

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