Tim Isbell, 2/2012

Sometimes we need to quickly generate an accurate graph of an equation, such as to check your manual solution of the equation or see how it responds to changes in the values of the constants.

A graphing calculator is a simple way to do this. A graphing calculator is a scientific calculator with a slightly larger screen and the ability to generate a graph on it. This means you can type in a function, such as f(x)=2^x and it will graph it for you. You can also type in several functions, such as a second function of f(x)=2^(x-2)+4, and it will graph this one on top of the first one so you can see the change very clearly. 

Handheld scientific graphing calculators are sold in stores and online, but they are a bit expensive. I bought a Ti-84 at Staples in 2011 for about $110. But graphing calculators are available online for free! You can google “graphing calculator” and find several. Some are too simple to do exponential equations, but others are even more powerful than the Ti-84.

Here's the URL for one that works fine: http://www.meta-calculator.com/online/. 

Below are some screen shots to show you how to use it.

So, type the URL into any browser and you should see the screen below.

 


Next: Click on Graphing Calculator. The next screen is below...

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You can see that I’ve typed in a few functions as an example of how things move around when the equation changes. Note that on your keyboard the exponent sign is the little ^ that is a "shift 6."

Okay, now at the bottom of the above screen click on Graph and you get the results below:

That's it! You can type in any equation and get the graph. In many classes students learn how to manually generate a graph of a basic function and then augment it to reflect the other complexities in the whole equation. These are very valuable skills to learn, but they are tedious to check. You can use a graphing calculator to check your hand analysis.

In addition, you can use a graphing calculator to solve 2 equations in 2 unknowns. You do this by programming the calculator to draw the two equations and where they intersect is your solution. Graphing calculators even have special functionality to help you find exactly the intersection points.