Graphing Calculators and You
Oh NO! They use graphing calculators all the time in the book, but my evil teacher won't let me use one on the test. How is that going to work?
I'm getting quite a few questions from people who are getting kind of worried, since the videos (and to a lesser extent, the textbook) use graphing calculators, and they are wondering (quite reasonably) how this is going to work on the test, or whether they are going to be "behind" in their math careers if they don't learn how to use one this semester.
Do I need to buy a graphing calculator for this class?
No, you don't. You will want to make use of graphing technology to explore the graphs in chapters 4 and 8, but you can just go to this online graphing calculator at Desmos. This will do pretty much everything a graphing calculator will do and will be eaiser to read. It's pretty easy to use and free, so I recommend it rather than buying a graphing calculator if you don't already have one.
How do I graph on the tests if a graphing calculator isn't allowed?
The graphing calculator/computer is a great tool to play around with and investigate more difficult graphs. However, don't kid yourself; you've got to know how to graph the trig functions on your own, without the help of a calculator or computer. That's what I will ask you for on the tests. I will expect you to know the graphs of the basic trig functions, along with changes of period, amplitude, reflections, and shifts. These are really important graphs and it's vital that you learn them for future classes.
How will all those graphing calculator type problems work on the test?
Remember, the whole point of the graphing calculator is to draw a graph. Tha's it. (Well, it can do a bunch more, but for most of what we are doing, that's it.) The real point of all those problems isn't how to make your calculator draw the graph, but for you to look at the graph and understand what it's telling you. So, if I want you to use a graph to answer a problem, I might give you something like this (this example is from algebra, but it works similarly for trig):
Solve |2x + 1| > 1 graphically.
Well, to work this, you need to know what the graph looks like. You could graph it by hand (not all that hard, but kind of a pain) or you could use your graphing calculator. On the test, this question might look something like this:
Use the graph of f(x)=|2x + 1| to solve the inequality |2x + 1| > 1:
So, I gave you the graph; now you need to figure out where the y values of this graph are > 1. (Hint: The answer is: x < -1 or x > 0.) So, the point isn't how you got the graph (in the first case, you would use your calculator to find it, while in the second case, I gave it to you), the point is to use the graph to answer the question.
Remember, the point is the graph, not the calculator or computer program; what does the graph tell you and how can you use the graph to help solve the problem? The calculator or computer program are just ways to draw that graph without having to do much work on your part (definitely a Good Thing).