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
• 𝑥𝑦 = 12
x
-4
3
6
y
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
• 𝑥𝑦 = 12
x
-4
3
6
y
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
• 𝑥𝑦 = 12
x
-4
3
6
y
For the relation given, complete the
table
• 𝑥𝑦 = 12
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
A) 𝑥 2 + 𝑥𝑦 = 4
B) 𝑥 + 𝑦 = 1
Equation A, test for y-axis
• 𝑥 2 + 𝑥𝑦 = 4
• (x,y)→(-x, y)
• (−𝑥)2 + −𝑥 𝑦 = ? = 𝑥 2 + 𝑥𝑦 = 4
• (−𝑥)2 + −𝑥 𝑦 = 𝑥 2 − 𝑥𝑦
• 𝑥 2 − 𝑥𝑦 ≠ 𝑥 2 + 𝑥𝑦
So no symmetry in the y-axis
The equation also fails the tests for the X-axis
and the line y=x
Equation A, test for origin
• 𝑥 2 + 𝑥𝑦 = 4
• (x,y)→(-x, -y)
• (−𝑥)2 + −𝑥 −𝑦 = ? = 𝑥 2 + 𝑥𝑦 = 4
• (−𝑥)2 + −𝑥 −𝑦 = 𝑥 2 + 𝑥𝑦
• 𝑥 2 + 𝑥𝑦 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