The 3CD course requires knowledge of domain, range, co-domain and inverse functions. The classpad can handle these in a number of ways.

The most obvious way is in graph mode (Menu-> graph tab). Set up a graph (say y=(x+1)/(x+2), and visually examine it to find the domain and range. To find the inverse, click on the graph and select Inverse (Analysis->Sketch->Inverse). The equation of the inverse can be found by selecting the inverse graph and examining the equation bar at the base of the screen. Be careful with this method, as the resultant inverse graph is not written in "y=" form.

The less obvious way to do it is in the main window. I have not found an "inverse" function yet, but the following is a workaround to find the inverse.

Go

Action->Transformation->Simplify (to simplify the resultant equation)

Action->Assistant->Invert (to swap the x & y variables around)

Action->Advanced->Solve (makes x the subject of the equation)

Enter the function

Press ",x)))" using the soft keyboard (to make x the subject of the new equation)

It would look something like this when finished:

simplify(invert(solve(y=((x+2)/3,x)))

In a way I prefer the main window method as it mirrors the algebraic method. I think students need to really understand the parts of an equation to effectively find the domain and range. I explicitly draw students attention to critical information such as the inability of the function to equal zero or where the function is undefined

a) Look for possible values of x where y=1/0 will occur (eg. {x≠-1} for y=1/(x+1) ).

b) If it is not possible for the numerator to be zero (eg. {y≠0} for y=2/(x+1))

If the range is not obvious it is often easier to examine the domain of the inverse of the function.

Here is a link to other CAS calculator posts.

Purplemath has a good explanation of inverse functions.

Thank you so much!

ReplyDeleteThis will be so useful for my VCE Maths Methods exam tomorrow!

:D

Any ideas for finding inverses for matrices? I could really use the help.

ReplyDeleteThank you

I'm sorry, matrices (other than for solving simultaneous equations) are part of the 3CD MAS course - the only WA course that isn't taught at our school. The stuff that I have done thus far is based around students needs in my courses.. I'd suggest to do a web search for Charlie Watson, he is the WA guru on calculator usage.

ReplyDelete