Study Notes
In algebra, transformations involve changing the position or size of graphs. These include translation, dilation, reflection, and rotation.
- Translation — A translation moves the graph up, down, and side to side. Example: Moving the graph of y = x up by 2 units results in y = x + 2.
- Dilation — A dilation makes the function skinnier or larger. Example: Multiplying y = x by 2 results in y = 2x, making it steeper.
- Reflection — A reflection is a mirror image that flips the function over the x or y axes. Example: Reflecting y = x over the x-axis results in y = -x.
- Rotation — A rotation involves turning the function around some axis by a certain degree. Example: Rotating y = x around the origin by 90 degrees changes its orientation.
Exam Tips
Key Definitions to Remember
- Translation: Moving a graph up, down, or sideways.
- Dilation: Changing the size of a graph, making it skinnier or larger.
- Reflection: Flipping a graph over an axis.
- Rotation: Turning a graph around a point.
Common Confusions
- Confusing translation with rotation.
- Mixing up dilation with reflection.
Typical Exam Questions
- What is a translation? A movement of the graph up, down, or sideways.
- How does a dilation affect a graph? It changes the size, making it skinnier or larger.
- What happens during a reflection? The graph is flipped over an axis.
What Examiners Usually Test
- Understanding of different types of transformations.
- Ability to apply transformations to various functions.