Translation
A graph can be translated in two ways, horizontally and vertically.
Horizontal Translation: When a graph is translated horizontally, each point on the graph moves left or right along the x-axis. The equation of the graph remains the same, but a constant value is added or subtracted from the x-coordinate of each point. For example, if we translate the graph of y = f(x) by c units to the right, the new equation becomes y = f(x − c).
Vertical Translation: When a graph is translated vertically, each point on the graph moves up or down along the y-axis. The equation of the graph remains the same, but a constant value is added or subtracted from the y-coordinate of each point. For example, if we translate the graph of y = f(x) by d units upward, the new equation becomes y = f(x) + d.
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