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Reflections and Symmetry Lesson 5.2

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Flipping the Graph of a Function Given the function below We wish to manipulate it by reflecting it across one of the axes Across the x-axis Across the y-axis

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Flipping the Graph of a Function Consider the function f(x) = 0.1*(x 3 - 9x 2 + 5) : place it in y1(x) graphed on the window -10 < x < 10 and -20 < y < 20

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Flipping 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-axis

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Flipping 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 about use -f(x) use f(-x) Spreadsheet Demo

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Even and Odd Functions If f(x) = f(-x) the graph is symmetric across the y-axis It is also an even function

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Even and Odd Functions If f(x) = -f(x) the graph is symmetric across the x-axis But... is it a function ??

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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 function

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Applications 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

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Applications This is the function f(x) = (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 the flip?

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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 points

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Reflecting in the Line y = x Results Note: it is not a function.

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Reflecting in the Line y = x Try it for this graph … will the result be a function or not?

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Assignment Lesson 5.2 Page 209 Exercises 1 – 31 odd

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