Reflections of Graphs

In relation to y = f(x);

It's useful to understand that;

y = -f(x) reverses the sign all of the function's $y$ -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.

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

REMEMBER that;

The graph of $y = f (x)$ is shown on the grid below.

zSqaD-pP_function

(a) On the grid, draw the graph of $y = f (- x)$ .

(b) On the grid, draw the graph of $y = - f (x)$ .

(a) Reflect in the y-axis

hntIoJJo_reflection-in-y-axis

(b) Reflect in the x-axis

efmZnBFc_reflection-in-x-axis

Reflections of Graphs (Edexcel GCSE Maths)