A graph is a type of picture that we can use to visualize ordered pairs, relations, and functions. Rather than force you to imagine what they might look like, we will use actual, physical diagrams that you can look and see right on your screen. No imagination necessary. You can tell the fairies and unicorns they can head on home.
The word "graph'' comes from the word "graphic, " which means having to do with pictures or writing. It has the same root as "graphite, " that stuff they make pencils from. It also has the same root as "graphitti, " which is what happen when taggers spray-paint mathematician's homes.