In this activity you will use a slider to change the basic (parent) functions. You will be able to change value of the sliders [math]a_0[/math], [math]a_i[/math], h, and k to transform the function by moving these sliders. The [math]r_0[/math] and [math]r_i[/math] allow your to reflect outside and inside of the function change you results. There are two check boxes to permit the user to easily demonstrate the results of a vertical or horizontal line test. The [math]a_0[/math] and the [math]a_i[/math] represent the effects of multipliers outside of the function f(x) and inside the parenthesis of f(x), sometimes these multipliers when used separately produce the same graph. When [math]a_0[/math] or [math]a_i[/math] are zero, the resulting graph is a constant function.[br][br] [math]g(x) = a_o f(a_i x – h) + k[/math][br][br][[b]Note[/b]: you may need to move a panel right to about 10 on x-axis.]

Your job is to determine the effects of each of the sliders on parent functions.[br]a) What does [math]a_o[/math] do to each function? Hint: its effects are the same for all functions.[br]b) What does [math]a_i[/math] do to each function?[br]c) What does h do in each function?[br]d) What does k do in each function?[br]e) What does [math]r_o[/math] do in each function?[br]f) What does [math]r_i[/math] do in each function?[br]g) Which axis is effected by the [color=#1551b5]blue[/color] sliders?[br]h) Which axis is effected by the [color=#c51414]red[/color] sliders?[br][br]Use these handouts as a guide to analyze the included functions.[br][br] Student worksheet (Original) [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Transformations_Families_of_Functions_Student.pdf]PDF[/url] [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Transformations_Families_of_Functions_Student.docx]DOCX[/url] [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Transformations_Families_of_Functions_Student.doc]DOC[/url].[br] Graph sketching guideline worksheets [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Graphing%20templateAlg2.pdf]Algebra II/Regular Precalculus[/url] [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Graphing%20templatePreCal.pdf]PreCalculs/Calculus[/url] (two templates per page)[br] New worksheet in process of completion[br][br]This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.