Reflections and SymmetryFlipping the Graph of a FunctionSlide 3Slide 4Slide 5Even and Odd FunctionsSlide 7Slide 8ApplicationsSlide 10Reflecting in the Line y = xSlide 12Slide 13AssignmentReflections and SymmetryLesson 6.2Flipping the Graph of a Function•Given the function below We wish to manipulate it by reflecting it across one of the axesAcross the x-axisAcross the y-axisFlipping the Graph of a Function•Consider the function f(x) = 0.1*(x3 - 9x2 + 5) : place it in y1(x)graphed on the window -10 < x < 10 and -20 < y < 20Flipping the Graph of a Function•specify the following functions on the Y= screen: y2(x) = y1(-x) dotted style y3(x) = -y1(x) thick style •Predict which of these will rotate the function about the x-axis about the y-axisFlipping the Graph of a Function•Results•To reflect f(x) in the x-axis or rotate about •To reflect f(x) in the y-axis or rotate aboutuse -f(x)use f(-x)Spreadsheet DemoSpreadsheet DemoEven and Odd Functions•If f(x) = f(-x) the graph is symmetric across the y-axis •It is also an even functionEven and Odd Functions•If f(x) = -f(x) the graph is symmetric across the x-axis •But ... is it a function ??Even and Odd Functions•A graph can be symmetric about a point Called point symmetry•If f(-x) = -f(x) it is symmetric about the origin •Also an odd functionApplications•Consider a frozen yam placed into a hot oven. Think what the graph of the temperature would look like. Sketch the graph of the temperature of the yam. It is frozen at 0 degrees Fahrenheit and the oven is at 300 degrees Fahrenheit.This will be both a flip and a shift of an exponential function This will be both a flip and a shift of an exponential functionApplications•This is the function f(x) = 300 - 300(0.97)t •It has been flipped about the y-axis •Then it has been shifted up •Which part did the shift?•Which part did theflip?Reflecting in the Line y = x•Given the function below:•For each (x,y) shown, reverse the values to get (y,x) •Plot the (y,x) values and connect the pointsReflecting in the Line y = x•Results•Note: it is not a function.Reflecting in the Line y = x•Try it for this graph … will the result be a function or not?Assignment•Lesson 6.2•Page 239•Exercises 1 – 39
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