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Reflections and Symmetry. Lesson 5.2. Across the x-axis. Across the y-axis. Flipping the Graph of a Function. Given the function below We wish to manipulate it by reflecting it across one of the axes. Flipping the Graph of a Function. Consider the function

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## Reflections and Symmetry

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**Reflections and Symmetry**Lesson 5.2**Across the x-axis**Across the y-axis Flipping the Graph of a Function • Given the function below • We wish to manipulate it by reflecting it across one of the axes**Flipping 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 < 20**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**use -f(x)**use f(-x) 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 Spreadsheet Demo**Even and Odd Functions**• If f(x) = f(-x) the graph is symmetric across the y-axis • It is also an even function**Even 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 function**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**Applications**• 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 points**Reflecting 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 5.2 • Page 209 • Exercises 1 – 31 odd

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