Graph of an Equation

What is the Graph of an Equation?

The set of points where the equation is true.

 

Example: y = x2 − 5

graph

We can plot some points where the equation is true:

x y = x2−5
−2 −1
0 −5
1 −4
3 4

 

Here we have a lot more points:

graph

And now the set of all points (within the range of the graph):

graph

 

Warning: Don't just plot a few points and think you have the graph!

Example: y = x3 − 5x

With these calculated points:

x y = x3−5x
−2 2
0 0
2 −2

We might think this is the graph:

graph

But this is the real graph:

graph

"Satisfy the Equation"

You may hear the phrase "satisfy the equation", which also means where the equation is true.

How To Graph

But this is just a help! They are only computer programs, and could easily miss some important thing on the graph, or not plot something correctly.

In fact they are not really "Complete" Graphs unless they show all features ...

A "Complete" Graph

For a graph to be "complete" we need to show all the important features.

Advanced Topic: Calculus (Finding Maxima and Minima using Derivatives) is a big help in finding important features.