MAC 1105
Project 1. Drawing with the Library of Functions.
Objectives:
- Identify the graphs and characteristics of the following functions:
- (greatest integer less than x) [ floor(x)]
- Identify and/or produce transformations of these function (translations, reflections, shrinking, stretching, etc.) varying the values of the parameters a, b, c, and d in the general expression .
Tasks.
- Become familiar with the graphing tool Desmos.
https://www.youtube.com/watch?v=_6-7Vp4oeKc&feature=emb_rel_end http://s3.amazonaws.com/desmos/Desmos_User_Guide.pdf.
- Use Desmos to graph the functions of the Library of Functions. (Functions a. to g.). Determine domain and range of each function. Graph the functions by restricting their domain to the interval (0,2)
- Consider the transformations for each function in the library. Analyze the effect of varying the values of each of the parameters. Report your results for each function and share them with your teammates.
- Draw general conclusions about the effect produced by the variation of each of the parameters.
- Make a drawing where you use all the functions of the Library of Functions (or transformations of them).
Report
You must submit a report (Word document) with the following points:
- For each of the functions a)-h) a) graph b) domain c) image d) intercepts e) symmetries
- For each of the parameters a,b,c,d in the general expression explain the effects of their variation. Specify the intervals of interest for the values of each parameter. For example: For b>0 ….. for b<0……. Or for 0<a<1……. For a>1…… etc. Illustrate your conclusions with graphical examples.
Example:.
The graph shows the graph of the function and . This example shows the effect of adding a positive constant to the output of the function We have a vertical shift of two units upward.
- Add your drawing. Explain in a general way the functions you used(with the corresponding transformations)
