Math 110
In Class Exercises, Section 2.1
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X
Symmetry: Graphically
Goal: Identify equations that are symmetric, and their type of symmetry
1) Does the graph to the left illustrate
an equation with any symmetry? If it
10
does, what symmetry does it illustrate?
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
2 3 4 5 6 7 8 9 10
X
Y
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
2) Does the graph to the left illustrate
an equation with any symmetry? If it
does, what symmetry does it illustrate?
2 3 4 5 6 7 8 9 10
Y
Math 110
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X
Math 110
In Class Exercises, Section 2.1
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
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3) Does the graph to the left illustrate
an equation with any symmetry? If it
does, what symmetry does it illustrate?
2 3 4 5 6 7 8 9 10
X
Y
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
4) Does the graph to the left illustrate
an equation with any symmetry? If it
does, what symmetry does it illustrate?
2 3 4 5 6 7 8 9 10
Y
Math 110
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Math 110
In Class Exercises, Section 2.1
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Symmetry: With Tables
Goal: Identify equations that are symmetric, and their type of symmetry – from a table!
Previously, you’ve seen something like this:
5) Given the points to the left, does the
equation that generated those points appear to
(0, 0), (2, 4), (6, 8), (10, 12), (-2, -4), (-6, -8), (-10,have any particular symmetry?
12)
We can also write the exact same information out
like, in a table of points:
X
0
2
6
10
-2
-6
-10
Y
0
4
8
12
-4
-8
-12
Table Of Points:
X
0
1
2
3
-1
-2
-3
Y
-1
1
7
17
1
7
17
If it does, what symmetry does it illustrate?
How do you know?
6) Given the points to the left, does the
equation that generated those points appear to
have any particular symmetry?
If it does, what symmetry does it illustrate?
How do you know?
Math 110
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Math 110
In Class Exercises, Section 2.1
Table Of Points:
X
0
2
6
10
-2
-6
-10
Y
0
4
8
12
-3
-7
-11
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7) Given the points to the left, does the
equation that generated those points appear to
have any particular symmetry?
If it does, what symmetry does it illustrate?
How do you know?
Table Of Points:
X
10
2
1
-1
2
1
10
Y
30
3
1
0
-3
-1
-30
8) Given the points to the left, does the
equation that generated those points appear to
have any particular symmetry?
If it does, what symmetry does it illustrate?
Is the relation that this table of ordered pairs
represents also a function? Explain why or why not:
How do you know?
Math 110
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Math 110
In Class Exercises, Section 2.1
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Symmetry: With Formulas
Goal: Identify equations that are symmetric, and their type of symmetry – from a table!
9) Is the following formula symmetric in any way? If so, how is it symmetric? How do you know?
y  x2  2
Show your work to test for the following types of symmetry:
x-axis
y-axis
origin
10) Is the following formula symmetric in any way? If so, how is it symmetric? How do you know?
y  x 6  3x 4  x 2  2
Show your work to test for the following types of symmetry:
x-axis
y-axis
Math 110
origin
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Math 110
In Class Exercises, Section 2.1
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11) Is the following formula symmetric in any way? If so, how is it symmetric? How do you know?
y  3x 8  3x 6  17 x 4  x 2  2
Show your work to test for the following types of symmetry:
x-axis
y-axis
origin
12) If an equation is a polynomial (it only has terms like 3x2, or 2x3 – nothing funky like absolute
value, etc), how can you quickly tell if it’s symmetric about the y-axis?
Why are functions that are symmetric about the y-axis called even functions?
Math 110
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Math 110
In Class Exercises, Section 2.1
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13) Is the following formula symmetric in any way? If so, how is it symmetric? How do you know?
y  x3  x
Show your work to test for the following types of symmetry:
x-axis
y-axis
origin
14) Is the following formula symmetric in any way? If so, how is it symmetric? How do you know?
y  2x 5  x 3  7 x
Show your work to test for the following types of symmetry:
x-axis
y-axis
Math 110
origin
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Math 110
In Class Exercises, Section 2.1
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15) Is the following formula symmetric in any way? If so, how is it symmetric? How do you know?
y  3x 9  3x 7  17 x 7  x 5  x 3
Show your work to test for the following types of symmetry:
x-axis
y-axis
origin
16) If an equation is a polynomial (it only has terms like 3x2, or 2x3 – nothing funky like absolute
value, etc), how can you quickly tell if it’s symmetric about the origin?
Why are functions that are symmetric about the origin called odd functions?
Math 110
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