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Description

A detailed tutorial on the translation of graphs. Step by step tutorial including several examples of translating graphs for reference.

Overview

There are different ways to translate graphs, but the easiest way is to memorize the general rules for translation. This tells you what parts of the equation do what to your basic graph. Starting with a graph of y = f(x), these would be your basic rules:

y = f(x – a) moves a units to the right

y = f(x + a) moves a units to the left

y = f(x) + a moves a units up

y = f(x) – a moves a units down

y = f(-x) reflects over the y-axis

y = -f(x) reflects over the x-axis

Reflections are always done before translations, not the other way around, because if you do your translation first you will end up with your shape having the wrong coordinates.