Pre-calc section 4-3 Reflections and symmetry part II

Pre-calc section 4-3

Reflections and symmetry part II

Describe any symmetry you notice

Reflect over the y-axis

Result of reflection

Reflect over the line y=x

Remember the name of each of these functions?

Using symmetry

• If the graph shown is part of a relation which has symmetry in the origin,

• Copy the graph, then sketch in the complete graph.

• Points on the graph incluced (5,0),(3,3),(2,4),and(1,8)

Using symmetry

• If the graph shown is part of a relation which has symmetry in the X and Y axes,

Symmetry in the Origin

Symmetry in just Y-axis

Symmetry in just X-axis

Symmetry both the X and Y axes

For the relation given, complete the table

Using symmetry

x y-4 3 or -3

3 4 or -4

6 2 or -2

Test each equation to see if it’s graph has symmetry

• Test X-axis, Y-axis, line y=x, and the origin

Equation A, test for y-axis

• (x,y)→(-x, y)

So no symmetry in the y-axisThe equation also fails the tests for the X-axis and the line y=x

Equation A, test for origin

• (x,y)→(-x, -y)

• is the original equation, So the graph does have rotational symmetry about the origin.

A) Symmetry in origin only

B) Symmetry in all 4 categories

Pre-calc section 4-3 Reflections and symmetry part II

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