Hope your Weekend was Relaxing!
 Pick up notes from the front table
Pick up new assignment log
Begin your Entry Ticket
 Tonight’s HW:
o Pg. 133 #2 ,3 15-29 odd, 39 AND draw a picture of a real life object that has
symmetry. Identify the point or line of symmetry please use graph paper.
o YOU NEED your graphing calculator for next class period or you will not
be able to participate in the activities and thus you will lose
participation points!
 Updates:
o Unit 3 Quiz 1 (3.1-3.2)
Thursday/Friday
Congratulations!
You made it through the first two units!!!
From now on, I am going to print your guided notes for
you 
Agenda
Entry Ticket! (Return quizzes)
3.1: Symmetry and Coordinate Graphs
Function Flash!
Cool-Down…
Notes/Homework Log
I am missing several homework logs and notes from
students.
This is effecting your grade. Please turn those in!
Return Work!
I am returning all work that I have of yours.
o The Unit 1 Projects will be handed back the Monday we
get back from break. ( graphing animals)
o Unit 2 Assessment will be returned Thursday/Friday (
hopefully!)
Entry Ticket
Learning Objectives
① Use algebraic tests to determine if the graph of a relation
is symmetrical.
② Classify functions as even or odds.
3.1 Symmetry and Coordinate Graphs
Unit 3 is all about the nature of graphs.
To help us sketch and analyze graphs in this unit we need to
understand types of symmetry.
3.1 Symmetry and Coordinate Graphs
Point Symmetry
o Two distinct points P and P’ are symmetric with respect to the
point of symmetry if
(1) the two distinct points are the same distance from the point of
symmetry AND
(2) they are opposite direction from one another.
3.1 Symmetry and Coordinate Graphs
In your tables:
 Identify the point of symmetry
for each figure.
 Use evidence to prove to me that
the King demonstrates point
symmetry.
 How many degrees will I have to
rotate to be symmetric about a
point?
3.1 Symmetry and Coordinate Graphs
Point Symmetry
o Two distinct points P and P’ are symmetric with respect to the
point of symmetry if
(1) the two distinct points are the same distance from the point of
symmetry AND
(2) they are opposite direction from one another.
o A figure that is symmetric with respect to a given point is
rotated 180°.
3.1 Symmetry and Coordinate Graphs
Whiteboards:
Using the definition of Point Symmetry, identify if the following
demonstrate point symmetry. If it does, provide the exact point.
(1)
(2)
(3)
3.1 Symmetry and Coordinate Graphs
Notice that both whiteboard (1) and (2) were symmetric about
(0,0) or the origin.
In your tables discuss the following:
o Specifically looking at the table, what do you notice about the
points when they are symmetric about the origin?
3.1 Symmetry and Coordinate Graphs
Symmetry with Respect to the Origin
If a graph is symmetric about the origin, it will demonstrate the
relationship f(-x) = - f(x).
Examples/ Non-Examples
3.1 Symmetry and Coordinate Graphs
Attempt Practice (1) using the definition of symmetry about the
origin.
3.1 Symmetry and Coordinate Graphs
We have discussed two types of symmetries so far:
① Point Symmetry
② Origin Symmetry
Now, let’s discuss line symmetry!
On your whiteboards, draw an example of line symmetry.
3.1 Symmetry and Coordinate Graphs
Line Symmetry
o Two distinct points P and P’ are symmetric with respect to a line
if the two points are reflected (or flipped) about the line.
o Figures or graphs that have line symmetry can be folded along
the line of symmetry so that the two halves match exactly.
o Some graphs have more than one line of symmetry.
3.1 Symmetry and Coordinate Graphs
Common line symmetries we see in graphs are with respect to the
x-axis, y-axis, y = x, and y = -x.
Whiteboards:
In your tables see if you can predict where the point (2, 4) will be
when symmetric with respect to:
x-axis
Hint: Keep in mind that symmetry must be
y-axis
the same distance from the pre-image to the
y=x
line and from the image to the line.
y = -x
3.1 Symmetry and Coordinate Graphs
Symmetry with Respect to:
x – axis: Point P(a, b) image would be P’(a, -b).
y – axis: Point P(a, b) image would be P’(-a, b).
y = x: Point P(a, b) image would be P’(b, a).
y = -x: Point P(a, b) image would be P’(-b, -a).
Reminder:
Absolute value:
-x = x
3.1 Symmetry and Coordinate Graphs
Let’s attempt (2a) together and then I am going to challenge you
with (2b). You can use your graphing calculator to look at the
function visually!
3.1 Symmetry and Coordinate Graphs
Common names you heard with symmetry in Algebra 2 were even
and odd.
o In your tables, discuss what you remember about even and odd
functions.
3.1 Symmetry and Coordinate Graphs
Even Functions
o Symmetric with respect to the y-axis.
o f(-x) = f(x)
0 Maps (x, y)  (-x, y)
0 Graph will match exactly if you fold “hotdog” style ( over the yaxis)
4
Real life logo:
2
-5
5
-2
-4
3.1 Symmetry and Coordinate Graphs
Odd Functions
o Symmetric with respect to the origin.
o Maps (x, y)  (-x, -y)
o f(-x) = -f(x)
0 Graph will match exactly if you fold the graph along the y-axis
(fold hot dog style). Then fold along the x-axis (hamburger
style).
0 It does NOT matter if you do hamburger first or hotdog first.
Real-life picture:
Neither Odd nor Even
Functions
Neither Odd nor Even
Functions
0 Any function that isn’t even or
odd
Part of Your Homework…
Is to draw a real life object and point out it’s symmetry so we are
going to practice with real life pictures. You may NOT use any of
the following pictures that I put on this PowerPoint for your
homework. BE CREATIVE!
For the following pictures identify the point or line of symmetry.
There may be none.
Part of Your Homework…
Is to draw a real life object and point out it’s symmetry so we are
going to practice with real life pictures. You may NOT use any of
the following pictures that I put on this PowerPoint for your
homework. BE CREATIVE!
For the following pictures identify the point or line of symmetry.
There may be none
Odd and Even Functions
0 Take out your whiteboards and whiteboard pens.
0 I am going to display a graph and you are going to write on your
whiteboard ODD, EVEN, or NEITHER.
0 ARE you READY?
0 GET SET!!
Odd and Even Functions
0 GO!!
Odd and Even Functions
Odd and Even Functions
Odd and Even Functions
Odd and Even Functions
Odd and Even Functions
Odd and Even Functions
Odd and Even Functions
Odd and Even Functions
Answer the following on your whiteboards:
You are given an ordered pair and you are to tell me where that
ordered pair will map to given it is part of an even function AND
given when it is part of an odd function.
(a) (5, 2)
(b) (-4, 4)
(c) (0, -3)
Whiteboards
Algebraically show that the following functions are even, odd, or
neither.
(a) h(x) = x3 – 1
(b) F(x) = 3x3
(c) d(x) = 2x3 – x
(d) k(x) = -3x4 – x2 + 2