If fx is any one of the six elementary trig functions, examine the role of the parameters a,b,h,k in the transformation a fbx−h+k.
tutor in the Student Precalculus package, as per the screen-shot in Table A-7.8(a).
Tools≻Tutors: Precalculus≻Standard Functions
Table A-7.8(a) Solution via the
tutor in the Student Precalculus package
, applied to the expression a sinb x−h+k, can also be used to obtain an interactive graph in which parameters can be varied. Figure A-7-8(a) shows the initial configuration for the Interactive Plot Builder; Figure A-7-8(b) shows the Options panel in which the "Range from/to" is set to limit the y-axis to the interval −10,10. Figure A-7-8(c) shows the Preview created by the Interactive Plot Builder. When the Plot button is finally selected, an interactive graph generated by the Explore command is inserted into the worksheet. (See below for additional details on this command.)
Figure A-7-8(a) Interactive Plot Builder - first pane
Figure A-7-8(b) Interactive Plot Builder - Options pane
Figure A-7-8(c) Interactive Parameter Maplet (Plot Builder Preview)
As an additional alternative, execute the following Explore command to activate the embedded probe of the sine function. Simply change the name of the function in the Explore command to explore the other trig functions.
Exploreplota sinb x−h+k,x=−2 π..2 π,y=−10..10,parameters=a=−5..5.0,b=−5..5.0,h=−2 π..2.0 π,k=−5..5.0,initialvalues=a=1,b=1,h=0,k=0,placement=right
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