Function Retrace 8A17D9
1. The problem is to find the equation of the retrace or reflection of a given function or curve.
2. The general formula for retracing or reflecting a function $y=f(x)$ about the x-axis is $y=-f(x)$, and about the y-axis is $y=f(-x)$.
3. Important rules:
- Reflection about the x-axis changes the sign of the output (y-values).
- Reflection about the y-axis changes the sign of the input (x-values).
4. For example, if the original function is $y=x^2$, then:
- Reflection about the x-axis: $y=-x^2$
- Reflection about the y-axis: $y=(-x)^2 = x^2$
5. This means the retrace about the x-axis flips the parabola upside down, while retrace about the y-axis leaves it unchanged for even functions.
6. To retrace a function, identify the axis of reflection and apply the corresponding formula.
Final answer depends on the original function and axis of retrace.