Reflections and Symmetry
Lesson 5.2
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
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)
 y3(x) = -y1(x)
dotted style
thick style
• Predict which of these will rotate the function
 about the x-axis
 about the y-axis
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)
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 the
flip?
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