Question

The function f(x)=x2 is transformed 3 times to become f(−x+4)+3 . Select the correct transformations below. (3 points) The function was translated 4 units (left/right) and 3 units (up/down) , and reflected over the (x/y) axis.

Answer 1

To analyze the transformation applied to the function \( f(x) = x^2 \) to become \( f(-x + 4) + 3 \), let's break it down step by step.

1. **Starting Function:** \( f(x) = x^2 \)

2. **Inside the Function: \( f(-x + 4) \)**
- The \(-x\) indicates a reflection over the **y-axis**.
- The \( +4 \) indicates a **horizontal translation**. Specifically, it shifts the graph to the **left** by 4 units (because you can think of this as translating the input by \( -4 \)).

3. **Outside the Function: \( +3 \)**
- This indicates a **vertical translation** of 3 units **up**.

Combining these transformations:

- The function is reflected over the **y-axis**.
- Then, it is translated **4 units left**.
- Finally, it is translated **3 units up**.

Hence, the correct transformations for \( f(-x + 4) + 3 \) are:
- **Reflected over the y-axis**
- **Translated 4 units left**
- **Translated 3 units up**

So the correct answer is:
- The function was translated 4 units left, 3 units up, and reflected over the y-axis (not the x-axis).