SYMMETRY GRAPHICAL REPRESENTATION

1. SYMMETRY GRAPH

2. “A graph is symmetric with respect to a line if
reflecting the graph over that line leaves the graph
unchanged. This line is called an axis of symmetry
of the graph.
2
2
SYMMETRIES OF A GRAPH

3. EXAMPLE
3
X
Y
Some Basic Example Of Symmetric

4. TYPES OF SYMMETRIES GRAPH
4
SYMMETRIES GRAPH
X-Axis
Symmetry
Y-Axis
Symmetry
Origin
Symmetry

5. 5
If an equation or function is symmetric with respect to the x-
axis. you can fold the paper it is graphed on along the x-Axis
and the halves of the graph will line up. If the ordered pair (x,
y) is a solution to the equation and the equation is symmetric
to the x-axis, then (x, -y) will also be a solution.
X-Axis Symmetry

6. Y-Axis Symmetry
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An equation or function that is symmetric with respect to the y-
axis has (x, y) and (-x, y) as solutions. Likewise, if you switch -x
for x in the original equation, the result should be the original
equation when simplified.

7. Origin Symmetry
7
Equations or functions that are symmetric to the origin
have ordered pairs (x, y) and (-x, y). If you switch -x for
x and -y for y in the original equation and simplify, if
you get the original equation, it is symmetric with
respect to the origin.

8. 8
Testing for symmetry
y= x2
y2 = x-1
1
X
X
Y
Y
y = x3 – x
= x(x2 -1)
= x(x-1)(x+1)
X
Y
(-y)2= x-1
y2 = x-1
f(x)= x2
f(-x)= (-x)2
y=x2
-y = (-x)3 – (-x)
-y = -x3 + x
Y = x3 - x

9. 9
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