1. Reflections and Symmetry
Lesson 5.2

2. 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

3. 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  < y < 20

4. 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

5. 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)
Spreadsheet Demo
use f(-x)

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

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

8. 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

9. This will be both a flip and a shift of an exponential 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

10. Applications This is the function It has been flipped about the y-axis
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?

11. 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

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

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

14. Assignment
Lesson 5.2
Page 209
Exercises 1 – 31 odd