Download presentation
Presentation is loading. Please wait.
Published byColin Gaines Modified over 9 years ago
1
3-1 Symmetry & Coordinate Graphs Objective: 1. To determine symmetry of a graph using algebraic tests. 2. To determine if a function is even or odd.
2
Point Symmetry Rotating a figure that has point symmetry 180 o should look the same.
3
Point Symmetry 2 points are symmetric with respect to (wrt) a 3 rd point “M” if & only if M is the midpoint of the 2 points. M
4
Point Symmetry The graph of a relation S is symmetric WRT the origin if and only if (a,b) S implies that (-a, -b) S.
5
Point Symmetry Steps for determining point symmetry about the origin: 1. Find f(-x) and –f(x) 2. If f(-x) =-f(x) then the graph has point symmetry.
6
Point Symmetry Example: Determine whether the graph is symmetric WRT the origin. .
7
Determine whether each graph is symmetric WRT the origin a) b)
8
Line Symmetry Two points P and P’ are symmetric wrt a line if and only if that line is the perpendicular bisector of PP’. A point P is symmetric to itself wrt a line if and only if P is on the line. Four cases we will look at: wrt x-axis wrt y-axis wrt y=x Wrt y=-x
9
Line Symmetry wrt x-axis If (a, -b) S and (a, b) S Substituting (a, b) and (a, -b) into the equation produces the same result.
10
Line Symmetry wrt x-axis Example: x = y 2 (4,2), (4,-2) are both members of this set
11
Line Symmetry- wrt y-axis If (-a, b) S and (a, b) S Substituting (-a, b) and (a, b) into the equation produces the same result.
12
Line Symmetry- wrt y-axis Example: y= x 2 -2 (-2, 2), (2, 2) are both members of this set
13
Line Symmetry- wrt y=x If (b,a) S and (a, b) S Substituting (b,a) and (a, b) into the equation produces the same result.
14
Line Symmetry- wrt y=x Example: xy= 12 ( 2,6), (6,2) are both members of this set
15
Line Symmetry- wrt y=-x If (-b,-a) S and (a, b) S Substituting (-b,-a) and (a, b) into the equation produces the same result.
16
Line Symmetry- wrt y=-x Example: xy= -12 ( 2,-6), (6,-2) are both members of this set
17
Practice Determine whether the graph of x 2 + y = 3 is symmetric with respect to the x-axis, the y-axis the line y = x, the line y = -x.
18
Practice: Can the graph of an equation be symmetric to more than one of these lines at a time? If yes, give an example, if no, give an explanation.
19
Practice Determine whether the graph of |y|=|x|+1 is symmetric with respect to the x-axis, the y-axis, both or neither. Use the information about the equation’s symmetry to graph the relation.
20
Even and Odd Functions Even functions have symmetry wrt the y-axis Odd functions have symmetry wrt the origin
21
Practice: Look at the previous examples from today and determine which are even or odd. even odd neither even odd
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.