Transformations of Graphs
Key points
- Transformations of graphs include vertical and horizontal translations, reflections, vertical and horizontal stretches.
- Multiple transformations performed on a function/graph are called composite transformations.
- These translations change the points on the graph of a function.
- When functions undergo transformations, their equation changes.
Graph transformations are processes that are performed on existing graphs, which result in modified graphs. As a result, the points on the line/curve change, and the equation does as well.
- Translations are when all of the points “slide” by a certain amount either vertically (up/down), or horizontally (left/right).
- The black graph undergoes a vertical translation of 5 units up and a horizontal transformation of 4 units right to become the purple graph.
- Reflections are when the individual points of the line are geometrically reflected over another line.
- Usually over the x or y axis.
- Stretches and compressions occur when the base graph is multiplied by a certain factor that affects how “tall” or “wide” it is.
- The black graph undergoes a vertical stretch by factor 3 to become the blue graph.
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