Question

Describe the transformations for the function y=−1x−2+3 .(1 point) Responses reflected across the y-axis, shifted up 3 units, and shifted right 2 units reflected across the y-axis, shifted up 3 units, and shifted right 2 units reflected across the x-axis, shifted up 3 units, and shifted left 2 units reflected across the x-axis, shifted up 3 units, and shifted left 2 units reflected across the x-axis, shifted down 3 units, and shifted left 2 units reflected across the x-axis, shifted down 3 units, and shifted left 2 units reflected across the x-axis, shifted up 3 units, and shifted right 2 units

Answer 1

To analyze the function \( y = -1(x - 2) + 3 \), let's rewrite it for clarity:

1. The equation can be interpreted as:
\[
y = -1(x - 2) + 3
\]

2. Start with the base function:
\[
y = x
\]

3. **Transformation Steps**:
- **Shift Right 2 Units**:
The term \( (x - 2) \) indicates a horizontal shift to the right by 2 units.

- **Reflect Across the X-Axis**:
The coefficient of -1 in front of the bracket indicates that the function is reflected across the x-axis.

- **Shift Up 3 Units**:
Finally, the +3 indicates a vertical shift upwards by 3 units.

In summary, the transformations for the function \( y = -1(x - 2) + 3 \) are:
- Reflected across the x-axis
- Shifted up 3 units
- Shifted right 2 units

Thus, the correct response is:
**Reflected across the x-axis, shifted up 3 units, and shifted right 2 units.**