The purpose of this lab is to become more familiar with Maple by using it to investigate manipulations of linear and quadratic functions.
The first part of this lab deals with linear functions, that is, functions of the form , where a and b are the slope and intercept. In Maple, it is easy to define both particular linear functions ( a and b are numbers) and general linear functions (a and b are parameters), as shown in the examples below.
> f := x -> x+2 ;
> g := x -> -2*x-3 ;
> h := x -> a*x+b;
The third example above shows how to form the composite function . The last example shows how to define a general linear function, where a and b are parameters.
In the exercises, you will need to know when two linear functions, say and are equal. This means that the equation is true for any value of x. ( More generally, two arbitrary functions and are equal if the equation is true for any value of x.) Geometrically, this means that the graphs of the two lines coincide. Since the equation of a linear function is determined by its graph, we can also say that two linear functions are equal if they have the same slopes and intercepts. For example, the two linear functions and we defined in the examples above are not equal, because their slopes and intercepts are not the same.
Now, suppose we wanted to choose values of a and b so that was equal to . Using the fact that the slopes and intercepts have to be the same, we see that we would have to choose a=1 and b=2.