Reflection across the -axis maps to and transforms into , while reflection across the -axis maps to and transforms it into . The distinction between changing input signs and output signs supports accurate interpretation and composition of function transformations; this scope does not include reflections across arbitrary lines or in higher dimensions.
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Detailed Explanation: Apply reflections across coordinate axes
To reflect a function’s graph, use the axis of reflection to decide which sign changes:
- Across the -axis: change the output sign.
- Across the -axis: change the input sign.
Worked example
Let
Find the equations of the graphs reflected across the -axis and the -axis.
1. Reflection across the -axis
Change the sign of the entire function:
Substitute the function:
Distribute the negative sign:
2. Reflection across the -axis
Replace every with :
Substitute into the function:
Simplify:
Remember: reflection across the -axis changes output signs, while reflection across the -axis changes input signs.
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Function Transformations (Definition) - Double Definition (Values) to Transformation
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This Worksheet Includes:
- Function Transformations (Definition) - Double Definition (Values) to Transformation
- Function Transformations (Vertex) - Double Transformed Vertex (Values) to Transformation
- Function Transformations (Vertex) - Double Transformation (Values) to Transformed Vertex
- Function Transformations (Definition) - Double Transformation (Variables) to Definition
- Function Transformations (Definition) - Double Transformation (Values) to Definition
- Function Transformations (Definition) - Single Definition (Variables) to Transformation
- Cartesian Grid - Reflection of Point (Coordinates to Coordinates) across Axis
- Function Transformations (Vertex) - Double Transformed Vertex (Variables) to Transformation
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