LOGARITHMIC FUNCTION – translation and scaling

 

In the second worksheet the graph of the logarithmic function, is presented DERIVE will be used to find out how translation and scaling affect the graphs of logarithmic functions. This exercise can be used with students already familiar with the basic graphs of logarithmic function.

Again in the introduction we briefly describe the necessary commands required to accomplish the tasks. We assume students already have some knowledge about the program, so the explanations are quite brief, intended just for those not so proficient in DERIVE. The teacher's introduction is still necessary as the function log x in DERIVE is not the common logarithm. The experience one teacher had when he (actually she) asked the students to graph the function log(x) and had of course the common logarithm in mind is presented in the cartoon below.

 

 

 

 

 

The exercise can be done in different settings regarding the time available and how familiar students are with DERIVE. Students can merely observe the teacher’s presentation and contribute their suggestions. If they are already more familiar with the program, they can fill in the worksheets in the computer lab or as part of their home assignments. Of course in the classroom a detailed analysis of their work has to be done.

 

What’s the exercise about? The students draw families of functions , , and . They try to describe the effect of parameter a. We expect them to get a feeling for what the graph of the function in the form looks like.

In the next lesson we have to cover the subject and state the findings, clearly subsequent lessons are then carried on classically, as according to our curriculum students must be cable to draw graphs of the functions without the computer or even without graphical calculators. The computer is used just to check the graphs.

 

The electronic form of the worksheet can be found on

 

http://rc.fmf.uni-lj.si/matija/logarithm/worksheets/graph.htm