Question
A) What is the order of combinations to transform f(x) = x
2
to f(x − 3) + 12? (1 point)
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 up 12 units.
Shift to the right 3 units and shift up 12 units
2
to f(x − 3) + 12? (1 point)
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 up 12 units.
Shift to the right 3 units and shift up 12 units
Answers
GPT-4o mini
To transform the function \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we can break it down step by step:
1. **Transforming to \( f(x - 3) \)**: This means we are shifting the graph of \( f(x) \) to the right by 3 units. When we replace \( x \) with \( x - 3 \), the graph moves to the right.
2. **Transforming to \( f(x - 3) + 12 \)**: Adding 12 means we are shifting the entire graph up by 12 units.
Putting these transformations together, we first shift to the right by 3 units, and then we shift up by 12 units.
Thus, the correct order of combinations is:
**Shift to the right 3 units and shift up 12 units.**
1. **Transforming to \( f(x - 3) \)**: This means we are shifting the graph of \( f(x) \) to the right by 3 units. When we replace \( x \) with \( x - 3 \), the graph moves to the right.
2. **Transforming to \( f(x - 3) + 12 \)**: Adding 12 means we are shifting the entire graph up by 12 units.
Putting these transformations together, we first shift to the right by 3 units, and then we shift up by 12 units.
Thus, the correct order of combinations is:
**Shift to the right 3 units and shift up 12 units.**