Keep using your function!
As you saw in the last activity, you were able to see that 1.5 times 2 take away 1 is 2 with the code
(1.5,f(1.5)). I've left that point visible below.
This is usually the time when readers start to get concerned about why they always have to type (#,f(#)) to see the results of their function. Well, you do not have to do this. You can just type f(1.5) in the input bar, but if you do this, you will create a "number object" in Geogebra, and "number objects" aren't plotted in the Graphics Mode in Geogebra (which is what is visible below). Number objects only show up in the Algebra Mode. We saw the Algebra Mode in this previous activity. For now, we're only looking at one mode at a time, but shortly we'll start seeing them both at the same time.
Before we do that though, it's important for you to get comfortable with the idea of plotting points on functions, so to that end, plot a few more points on f(x) by typing (#,f(#)). Its also a good idea to try plotting a point not on f(x) with code like (2,f(2+0.1)). The point is close to, but not quite on f(x). We can bring the point back onto the graph of f(x) by adding 0.1 to the input, with code like (2+0.1,f(2+0.1)).It might be worth noting, this particular type of function is called a
f(x)=mx+b
where m and b can be any numbers, like 2 and -1.
I expect you to know a little bit about lines in the rest of this book. For instance, I hope you remember that m is the slope of a line, and b is the y-intercept of a line. All that knowledge you have about lines will come in handy later. If you need a review, I recommend Saul Khan's summary of lines here.
Linear functions are tremendously important in calculus, and we'll encounter them quite a few times.
We should probably pause for a moment and discuss what a function actually is. Let's do that in the next activity. Click ahead when you're ready.