Question
The function f(x)=x2 is transformed 3 times to become f(−x+4)+3. Place the transformations in the order in which they occurred.
Type 1 for: translate left 4 units
Type 2 for: translate up 3 units
Type 3 for: reflect over the x-axis
Type 1 for: translate left 4 units
Type 2 for: translate up 3 units
Type 3 for: reflect over the x-axis
Answers
GPT-4o mini
To analyze the transformations of the function \( f(x) = x^2 \) to become \( f(-x + 4) + 3 \), we need to understand the changes step-by-step:
1. **Reflect over the x-axis**: The transformation from \( f(x) \) to \( f(-x) \) involves reflecting the graph over the x-axis. This is the first transformation.
2. **Translate left 4 units**: The transformation from \( f(-x) \) to \( f(-x + 4) \) means we are translating the graph 4 units to the left. This is the second transformation.
3. **Translate up 3 units**: The final step involves translating \( f(-x + 4) \) upward by 3 units to get \( f(-x + 4) + 3 \). This is the third transformation.
Putting them in the order they occurred, we have:
1. Type 3: reflect over the x-axis
2. Type 1: translate left 4 units
3. Type 2: translate up 3 units
So the order of transformations is: **3, 1, 2**.
1. **Reflect over the x-axis**: The transformation from \( f(x) \) to \( f(-x) \) involves reflecting the graph over the x-axis. This is the first transformation.
2. **Translate left 4 units**: The transformation from \( f(-x) \) to \( f(-x + 4) \) means we are translating the graph 4 units to the left. This is the second transformation.
3. **Translate up 3 units**: The final step involves translating \( f(-x + 4) \) upward by 3 units to get \( f(-x + 4) + 3 \). This is the third transformation.
Putting them in the order they occurred, we have:
1. Type 3: reflect over the x-axis
2. Type 1: translate left 4 units
3. Type 2: translate up 3 units
So the order of transformations is: **3, 1, 2**.