Subjects algebra

Function Retrace 8A17D9

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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.