Function Graphs

Function Theory (Lesson 2/6)

1 / 24

A graph is a powerful way to visualize the behavior of a function. To see how, let's start with a super basic example:

From the diagram above we see that

f(6)=3
f(8)=0
f(−9)=−1

If we call the input of the function x, and name the output y=f(x), then each input-output pair becomes a point:

f(6)=3(6,3)

f(8)=0(8,0)

f(−9)=−1(−9,−1)

We can then plot these points on the cartesian plane:

In summary, the graph of a function shows all the points (input,output), with the x-axis representing the inputs and the y-axis representing the outputs.