Lesson on graphing functions

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Quadratic Function (Parabola)

Two Linear Functions


Major Steps of Graphing

This lesson has two major parts, easy and advanced. Whenever you need to draw a graph, you always need to follow the following guidelines.

How to plot a nice graph with sweaty shaky hands

I have to make a terrible confession. My hands are sweaty and they shake a lot. I am generally a messy person and my wife complains that my desk is a nightmare. Maybe she is right. But my experiences taught me how to plot nice graphs.

  • Take your time. I had to learn it the hard way, whenever I took a shortcut I had to spend a lot of time fixing my mistakes.
  • Use a ruler.
  • Use a pencil, not a pen, it is easier to erase
  • Plot with small strokes of your pencil. Do not try to plot the entire graph in one move of your hand.

This hilarious picture taken from Purplemath
(link opens in a separate window)

Determining the nature of the function you are graphing

Jump to: Linear (straight lines) , Quadratic (parabolas) , Absolute value

Remember that the high school curriculum is designed so that even relatively stupid students can get decent grades, provided that they spend time doing homework and read textbooks. So in most schools, you will not be asked to plot very fancy graphs.

This chapter helps you do 90% of your graphing homework by jumping to the appropriate type of graphs. For those of you who study advanced math, or are curious, more explanations are provided in the advanced sections of this lesson.

You can expect graphs of the following type:

Linear Functions. They are represented by straight lines. They are given by equations such as


Their graphs are always represented by a straight line. You have to use a ruler to plot them. They look like this:

graph of a linear function

Quadratic Functions. They are represented by parabolas, which are curvy (not straight) lines sort of like cow horns. By the way, if you throw a rock, its line of fall is represented by a parabola (with horns obviously pointing down). Try it where windows and people are not in danger. Parabolas represent quadratic equations such as


Because parabolas are curvy, you cannot use a ruler to plot them. They look like this:

Parabola -- graph of a linear function

Absolute Values. In simple cases, they are represented by jagged lines composed of straigt segments. In more complicated cases, where the absolute value is mixed in with other functions, the lines may be not straight, however they have still some points where the graphs are not smooth and where the tangent angle changes abruptly. An example of a simple graph involving absolute value is


You can use a ruler to plot simple absolute value graphs, however you have to find where the straight lines break. The graphs look like this:

typical graph of an
	     absolute value

Advanced Graphing

Next: >> Click Here for an advanced graphing lesson