2 Sound Waves Consider a sound wave Place the function in your Y= screen Represented by the function y = sin x) Place the function in your Y= screenMake sure the mode is set to radiansUse the ZoomTrig optionThe rise and fall of the graph model the vibration of the object creating or transmitting the sound.What should be altered on the graph to show increased intensity or loudness?
3 Sound WavesTo model making the sound LOUDER we increase the maximum and minimum values (above and below the x-axis)We increase the amplitude of the functionWe seek to "stretch" the function verticallyTry graphing the following functions. Place them in your Y= screenFunctionStyley1=sin xy2=(1/2)*sin(x)y3=3*sin(x)dottedthicknormalPredict what you think will happen before you actually graph the functions
4 Sound Waves Note the results of graphing the three functions. The coefficient 3 in 3 sin(x) stretches the function verticallyThe coefficient 1/2 in (1/2) sin (x) compresses the function vertically
5 CompressionThe graph of f(x) = (x - 2)(x + 3)(x - 7) with a standard zoom graphs as shown to the right.Enter the function in for y1=(x - 2)(x + 3)(x - 7) in your Y= screen.Graph it to verify you have the right function.
6 CompressionWhat can we do (without changing the zoom) to force the graph to be within the standard zoom?We wish to compress the graph by a factor of 0.1Enter the altered form of your y1(x) function into y2= your Y= screen which will do this.
7 CompressionWhen we multiply the function by a positive fraction less than 1,We compress the functionThe local max and min are within the bounds of the standard zoom window.
8 View the different versions of the altered graphs Changes to a GraphWhat has changed?What remains the same?View the different versions of the altered graphs
9 Changes to a GraphClassify the following properties as changed or not changed when the function f(x) is modified by a coefficient a*f(x)PropertyChangedNot ChangedZeros of the functionIntervals where the function increases or decreasesX locations of the max and minY-locations of the max and minSteepness of curves where function is increasing/decreasing
10 Changes to a GraphConsider the function below. What role to each of the modifiers play in transforming the graph?ModifierResultabcd
11 Combining Transformations y = a * f (b * (x + c)) + da => vertical stretch/compression|a| > 1 causes stretch-1 < a < 1 causes compression of the grapha < 0 will "flip" the graph about the x-axisb => horizontal stretch/compressionb > 1 causes compression|b| < 1 causes stretching
12 Combining Transformations y = a * f (b * (x + c)) + dc => horizontal shift of the graphc < 0 causes shift to the rightc > 0 causes shift to the leftd => vertical shift of the graphd > 0 causes upward shiftd < 0 causes downward shift