SYMMETRY GRAPH.pptx

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 6 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= x 2 y 2 = x-1 1 X X Y Y y = x 3 – x = x(x 2 -1) = x(x-1)(x+1) X Y (-y) 2 = x-1 y 2 = x-1 f(x)= x 2 f(-x)= (-x) 2 y=x 2 -y = (-x) 3 – (-x) -y = -x 3 + x Y = x 3 - x

9. 9 Thank You