Graph Transformations

Tags

math

Largely divided into 4 transformations:

• Translation
• Enlargement \(\longrightarrow\) Stretching
• Reflection
• Rotation

If we define a graph \( y = f(x) \), then

• \( y = -f(x) \) creates a reflection of the graph on the y-axis.
• \( y = f(-x) \) creates a reflection of the graph on the x-axis.
• \( y = f(x+z) \) pushes the graph by \( -z \) on the x-axis.
• \( y = f(x)+z \) pushes the graph by \( z \) on the y-axis.

The order of one \( x \) or one \( y \) graph transformation can be applied in any order, however multiple y-transformations should be applied in BIDMAS order and multiple x-transformations should be applied in reverse-BIDMAS order.