Transformation (Algebra 1)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
In Algebra 1, the term transformation typically refers to changes made to the graph of a function or equation through various operations. These transformations alter the position, shape, or size of the graph in a systematic way. Common types of transformations include:
Translation: Shifting the graph of a function horizontally or vertically without changing its shape or size.
Vertical translation: Moving the graph up or down (e.g., f(x) + c).
Horizontal translation: Moving the graph left or right (e.g., f(x - c)).
Reflection: Flipping the graph over a specific line, typically the x-axis or y-axis.
Reflection across the x-axis: The graph is flipped vertically (e.g., -f(x)).
Reflection across the y-axis: The graph is flipped horizontally (e.g., f(-x)).
Stretching and Shrinking (Scaling): Changing the size of the graph either vertically or horizontally.
Vertical stretch/compression: If you multiply the function by a constant (e.g., af(x), where a>1 stretches the graph, and 0 < a < 1 compresses it.
Horizontal stretch/compression: Involves manipulating the function inside the parentheses (e.g., f(bx)), where |b| > 1 compresses the graph horizontally, and 0 < |b| < 1 stretches it.
Each of these transformations maintains the general shape of the graph but modifies its position, size, or orientation. Understanding transformations in Algebra 1 helps to better grasp how functions behave when altered by different operations.