Transformation

Definition

Transformation in algebra involves changing the position, shape, or size of a function's graph. Common transformations include translations, reflections, stretches, and compressions.

5 Must Know Facts For Your Next Test

1. A vertical translation moves the graph up or down by adding or subtracting a constant.
2. A horizontal translation shifts the graph left or right by adding or subtracting a constant inside the function's argument.
3. Reflection across the x-axis is achieved by multiplying the function by -1.
4. Vertical stretches and compressions are applied by multiplying the entire function by a constant greater than 1 or between 0 and 1, respectively.
5. Horizontal stretches and compressions involve altering the input variable with constants; for example, $f(2x)$ compresses while $f(\frac{x}{2})$ stretches.

Review Questions

• How does adding a constant to a function affect its graph?
• What transformation occurs when you multiply a function by -1?
• Explain how you would stretch a function horizontally.

Related terms

Translation: Shifting the graph of a function horizontally or vertically without altering its shape or orientation.

Reflection: Flipping the graph of a function over a specified axis.

Stretch/Compression: Altering the width or height of the graph of a function by multiplying inputs or outputs by constants.