Question

What is the order of combinations to transform f(x)=x^2 to f(x-3)+12
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 left 3 units and shift up 12 units
Shift to the left 3 units and shift down 12 units

Answer 1

To transform the function \( f(x) = x^2 \) to \( f(x-3) + 12 \), let's analyze the transformations step by step.

1. **Shift to the right by 3 units**:
- The transformation this accounts for is changing \( x \) to \( x - 3 \), which gives us \( f(x-3) = (x-3)^2 \).
- This shifts the entire graph of \( f(x) = x^2 \) to the right by 3 units.

2. **Shift up by 12 units**:
- After shifting the graph to the right, we then add 12 to the entire function, resulting in \( f(x-3) + 12 = (x-3)^2 + 12 \).
- This shifts the entire graph upward by 12 units.

Therefore, the correct order of the transformations to go from \( f(x) = x^2 \) to \( f(x-3) + 12 \) is:

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

So, the correct choice of combination is:

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