Reflections of Graphs (AQA GCSE Maths)

How do we reflect graphs of functions?

In relation to y = f(x);

• y = -f(x) represents a reflection in the x-axis (up/ down)
• y = f(-x) represents a reflection in the y-axis (left/ right)

How do reflections of graphs work?

It's useful to understand that;

• y = -f(x) reverses the sign all of the function's -coordinates: that's why it gets reflected in the up/down direction.
• Similarly, y = f(-x) reverses the sign of all the of the function's x-coordinates: that's why it gets reflected in the left/right direction.

How do we describe reflections of graphs?

• Some questions give a transformed function in the form y = f(−x) or y = −f(x) and ask you to describe the transformation
• To describe a reflection fully, you must include;
  1. the transformation: "reflection"
  2. the direction; in the x-axis or in the y-axis
• Remember that
  • if the "−" is inside the bracket, its a reflection in the y-axis
  • if the "−" is outside the bracket, its a reflection in the x-axis