how do you do a step function graph?

Answer 1

Usually "step function" refers generally to any function that is split into parts. You graph each function separately, but only show that part of the graph for which the function is defined as part of your step function. For instance, if your function said

x - 2 , x < 3
x^2 , 3 <= x < 5
5x , x > 5

you'd have parts of two lines at the beginning and end and part of a parabola in the middle.

Typically each "step" (portion of the graph) is shown with an open circle at endpoints that are not included (where the definition uses just < or just >) and closed dots at endpoints that are included (with <= or >= in the definition).

A "true" step function (one that literally looks like stair steps) is just a bunch of horizontal line segments with circles at one end and dots at the other. An example of such a function is the greatest integer function INT(X), which gives the value of the greatest integer less than or equal to any number.