Adv. Math: Chapter 3
Lesson 3-1: Symmetry and
Coordinate Graphs
Objectives:
- Use algebraic tests to determine if the graph of a relation is symmetrical
- Classify functions as even or odd
**Use the “rules” of symmetry to help sketch and analyze graphs. **
Point Symmetry – Two distinct points P and P’ are symmetric with respect to point M
if and only if M is the midpoint of PP’. Point M is symmetric with respect to itself.
**Look at pg. 127 . . . .
Symmetry w/ Respect to the Origin – A function has a graph that is symmetric with
respect to the origin if and only if f(-x) = -f(x) for all x in the domain of f.
**The graph of a relation S is symmetric with respect to the origin if and only if
implies that
means the ordered pair (a, b) belongs to the solution set S
Ex. 1: Determine whether each graph is symmetric with respect to the origin.
a) b)
c)
Line Symmetry – Two distinct points P and P’ are symmetric with respect to a line l
if and only if l is the perpendicular bisector or PP’. A point P is symmetric to itself
with respect to line l if and only if P is on l.
Common Lines of Symmetry:
/ Rules . . . .
continued . . .
Ex. 2: Determine whether the graph of xy = -2is symmetric with respect to the x-axis,
y-axis, the line y = x, the line y = -x or none of these.
x-axis →
y-axis →
y = x →
y = -x →
Ex. 3: Determine whether the graph of is symmetric with
respect t the x-axis, the y-axis, both, or neither. Use the information about the
equation’s symmetry to graph the relation.
x- axis →
y-axis →
Even vs Odd Functions:
Even Functions -
Odd Functions -
Homework: