Review Graphing

Graphs that you may encounter:

Quadratic Function (Parabola)

Two Linear Functions

2.5*sin(x2)

How to make a nice graph:

Even someone as messy and uncoordinated as Patrick Star can make a nice graph with there few things:

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.

If hand drawn graphs are not your forte, use a graphing calculator!

Understand the graph:

Before Spongebob cooks patties, he must understand his love for cooking at the Krusty Krab. Therefore, to make a graph you must understand its nature.

You can expect graphs of the following type:

Linear Functions. They are represented by straight lines. They are given by equations such as
y=3x-6
Their graphs are always represented by a straight line. You have to use a ruler to plot them. They look like this:




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

y=x2+4x+3


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



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

y=x-1


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:


Rules to graphing:

BY HAND:
1. A good mathematician knows that to graph, you need coordinates.
(x, y)
The x value is the number on the horizontal axis, while the y value is on the vertical axis. Follow the values of both variables until their continuous paths meet. That meeting point is your first graphed coordinate.

2. You can trace the values of a coordinate by means of a table of values with a pattern

3. Use hand drawn graphs as a way of helping you sort through your logic. Don't depend on them to be accurate.

BY CALCULATOR:
*Refer to TI NSPIRE Graph or TI 84 Graph