Reflections and Symmetry

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# Reflections and Symmetry - PowerPoint PPT Presentation

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

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

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

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