Transformation

Definition

Transformation refers to any operation that moves or changes a function in some way. Common transformations include translations, dilations, reflections, and rotations.

5 Must Know Facts For Your Next Test

1. A vertical translation moves a graph up or down without changing its shape.
2. A horizontal translation shifts a graph left or right and is represented by adding or subtracting inside the function's argument.
3. Reflections flip a graph over a specific axis; reflecting over the x-axis involves multiplying the function by -1.
4. Vertical stretches and compressions involve multiplying the entire function by a constant factor greater than 1 (stretch) or between 0 and 1 (compression).
5. Combined transformations can be applied in sequence; for example, reflecting followed by translating.

Review Questions

• What effect does adding a constant outside of the function have on its graph?
• How would you reflect a function \( f(x) \) over the y-axis?
• Describe how you would vertically stretch the graph of \( f(x) \) by a factor of 3.

Related terms

Translation: A transformation that shifts a graph horizontally, vertically, or both without altering its shape.

Reflection: A transformation creating a mirror image of the original graph across an axis.

Dilation: A transformation that stretches or compresses the graph of a function vertically or horizontally.