Pre-calc section 4-3 Reflections and symmetry part II.
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Transcript of 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
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