1.Graph the following polynomial functions: f(x)=(x-2)(x-1)²(x+1)²(x+3)

2.Graph f(x) = 2x/(x+2)

3.Graph f(x) = 1-x² and g(x)=1/(1-x²) on the same set of axes.

The first thing to do, if possible, is to find the roots of the equation. In your first example



The roots are x=2, 1, 1, -1, -1, -3. These are the points where the graph crosses zero.

If you can't get the roots easily, don't worry about it, just follow along.

Make two columns of numbers. On the left create a series of numbers. Make sure they span the roots an extend somewhat past those roots. In the first example, roots go from -3 to +2 so I'd suggest graphing from at least -4 to +3.

For each number you select to graph, plug it into the equation. In #1, again, let's select -4

x=-4;

You now have an "xy pair".
Once you have your points, simply plot the xy pairs on graph paper. You can also do this with Excel or another spreadsheet program. Open Office has a spreadsheet in it, and it's free.

OpenOffice.org - The Free and Open Productivity Suite

This was done with Excel. Note that it's the same data, but it's been plotted at different scales.

Attached Images

 

Don't you have a calculator or some other graphing utility? Here is a free one that is great. I use it all the time. It graphs in standard, polar, and parametric. Finds area, arc length, and has other nice features. I recommend it.

Graph