mirror image
[mirror image|mirror image] A mirror image is a reflection that produces a mirrored version of the original graph, either horizontally or vertically.
Definition
mirror image A mirror image is a reflection that produces a mirrored version of the original graph, either horizontally or vertically. Horizontal reflection mirrors about the y-axis, while vertical reflection mirrors about the x-axis.
Mechanism
mirror image The horizontal reflection creates a mirror image of the original graph about the y-axis. Each point on the graph of a function f(x) corresponds to a mirror image on the graph of f⁻¹(x). This relationship is established through the line y = x, which serves as the axis of reflection. The mirror image property ensures that graphs of inverse functions are symmetric with respect to this line.
Causes
mirror image The horizontal reflection produces a mirror image of the base graph about the y-axis. The vertical reflection creates a mirror image of the original graph about the x-axis. Both reflections generate mirror images through axis-based transformations. Notice that these transformations result in mirror images by flipping the graph across specified axes.
Every Point Mechanism
mirror image In the context of function graphs, every point on the graph of f(x) corresponds to a mirror image on the graph of f⁻¹(x). This relationship is established through reflection across the line y = x, making the graphs mirror images of each other. The term 'mirror image' describes this exact symmetry between points on the two graphs. Each point's reflection ensures the graphs maintain their inverse relationship. This mechanism is fundamental to understanding how inverse functions are visually represented.
Horizontal Reflection
mirror image is a horizontal reflection that produces a mirror image of the original graph by flipping it across the y-axis. This transformation generates a mirror image by reflecting the original graph over the y-axis.
New Graph
mirror image is a new graph created by horizontally reflecting the original graph across the y-axis. This reflection produces a mirror image that is symmetrical to the original graph.
Vertical Reflection
mirror image is a vertical reflection that creates a mirror image of the original graph across the x-axis. This transformation results in a symmetrical counterpart with the same shape but inverted vertically.