Horizontal Stretches and CompressionManipulating a FunctionSlide 3Changes to a GraphChanges to a TableSlide 6Slide 7Slide 8Functions Where Formula Not KnownSlide 10AssignmentHorizontal Stretches and CompressionLesson 6.4Manipulating a Function•Given the function for the Y= screeny1(x) = 0.1(x3 – 9x2)Use window -10 < x < 10 and -20 < y < 20•Now do the transformationy2(x) = y1(.5x)y3(x) = y1(3x)Make predictions for what will happenMake predictions for what will happenSet the styles differentManipulating a Function•For Horizontal stretch Horizontal compressionOriginal f(x)( )y f a x= �0 < a < 1a > 1f(0.5x)stretchedf(3x)compressedChanges to a Graph•Consider once again the effect of modifiers•For this lesson we are concentrating on b•b => horizontal stretch/compression b > 1 causes compression |b| < 1 causes stretching( ( ))y a f x cb d= � � + +Note Science Illustration on the WebNote Science Illustration on the WebChanges to a Table•Try these functionsy1(x) = 3x2 – 2xy2(x) = y1(0.5 x)y3(x) = y1(2x)•Go to tables (Y), then setup, F2Table start = - 4Table increment = 1Changes to a Table•Note the resultsf(x)f(0.5x)f(2x)StretchedCompressedChanges to a Graph•View the different versions of the altered graphs What has changed?What remains the same?What has changed?What remains the same?Changes to a Graph•Classify the following properties as changed or not changed when the function f(x) is modified by a coefficient f(b*x)Property ChangedNot ChangedZeros of the function Intervals where the function increases or decreases X locations of the max and min Y-locations of the max and minSteepness of curves where function is increasing/decreasingFunctions Where Formula Not Known•Given a function defined by a tableFill in all possible blanksx -3 -2 -1 0 1 2 3f(x) -4 -1 2 3 0 -3 -6f(.5x)f(2x)Functions Where Formula Not Known•Given f(x) defined by graph below•Which is f(2x)? 2*f(x)? f(0.5x)?Assignment•Lesson 6.4•Page 253•Exercises 1 – 27
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