Pre-calc section 4-3

Reflections and symmetry part II

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

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,

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

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

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

x y-4

3

6

Pre-calc section 4-3

Reflections and symmetry part II

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

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,

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

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

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

x y-4

3

6

Pre-calc section 4-3

Reflections and symmetry part II

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

Describe any symmetry you notice

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,

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

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

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

x y-4

3

6

For the relation given, complete the table

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