Properties of Graph Transformations
Graph transformations exhibit several properties that are important to understand when manipulating graphs. Here are some key properties:
- Preservation of Shape: Most graph transformations preserve the basic shape of the original graph. For instance, a translation or rotation does not change the overall shape of the graph, but simply moves or rotates it.
- Preservation of Slope: Some transformations, such as translations and scalings, preserve the slope of the original graph. For example, if a function has a constant slope, it will maintain that slope after a translation or scaling.
- Preservation of Length: Certain transformations, like translations and rotations, preserve the lengths of line segments and curves on the graph. This means that distances between points on the original graph remain unchanged.
- Effect on Intercepts: Transformations can affect the intercepts of a graph. For example, a vertical translation will change the y-intercept of a function, while a horizontal translation will change the x-intercept.
- Symmetry: Some transformations introduce symmetry into the graph. For example, a reflection across the x-axis or y-axis creates symmetry with respect to that axis.
- Orientation: Transformations like rotations change the orientation of the graph. For example, a clockwise rotation will change the orientation of the graph compared to a counterclockwise rotation.
- Effect on Domain and Range: Certain transformations may affect the domain and range of the function represented by the graph. For example, a vertical scaling may stretch or compress the range of the function.
Graph Transformations
Graph transformations involve changing the appearance or position of graphs by shifting them horizontally or vertically, stretching or compressing them, reflecting them across axes, or rotating them around a fixed point. These modifications help visualize how functions change under different conditions or transformations.
In this article, we will learn the meaning of graph transformations, the types of graph transformations, and properties of graph translations.
Table of Content
- What is Transformations of Graph?
- Types of Graph Transformations
- Translation
- Reflection
- Scaling (Dilation)
- Rotation
- Shearing
- Properties of Graph Transformations