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Example Questions
Example Question #1 : Graphing Functions
If , what kind of symmetry does the functionÂ
 have?
Symmetry across the line y=x
Even Symmetry
No Symmetry
Odd Symmetry
Even Symmetry
The definition of even symmetry is ifÂ
Example Question #1 : Graphing Functions
If , what kind of symmetry doesÂ
 have?
Odd symmetry
Even symmetryÂ
No symmetry
Symmetry across the line y=x
Odd symmetry
 is the definition of odd symmetry
Example Question #1 : Determine The Symmetry Of An Equation
Is the following function symmetric across the y-axis? (Is it an even function?)Â
Â
Cannot be determined from the information givenÂ
YesÂ
This isn't even a function!Â
I don't know anything about this function.Â
No
No
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute  in forÂ
. When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.Â
For our function:Â
Thus the function is not symmetric about the y-axis.Â
Example Question #1 : Determine The Symmetry Of An Equation
Is the following function symmetric across the y-axis? (Is it an even function?)Â
I don't know!Â
YesÂ
NoÂ
There is not enough information to determine
That's not a function!Â
YesÂ
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute  in forÂ
. When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.Â
For our function:Â
Since this matches the original, our function is symmetric across the y-axis.Â
Example Question #3 : Determine The Symmetry Of An Equation
Determine if there is symmetry with the equation  to the
-axis and the method used to determine the answer.
In order to determine if there is symmetry about the x-axis, replace all  variables withÂ
. Â Solving forÂ
, if the new equation is the same as the original equation, then there is symmetry with the x-axis.
Since the original and new equations are not equivalent, there is no symmetry with the x-axis.
The correct answer is:
Example Question #1 : Determine The Symmetry Of An Equation
Is the following function symmetrical about the y axis (is it an even function)?
Not a function
No
Insufficient Information
Yes
No
For a function to be even, it must satisfy the equalityÂ
Likewise if a function is even, it is symmetrical about the y-axisÂ
Therefore, the function is not even, and so the answer is No
Example Question #5 : Determine The Symmetry Of An Equation
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
No symmetry
Symmetrical about the y-axis
Symmetrical about the origin
Symmetrical about the x-axis
Symmetrical about the x-axis
For a function to be symmetrical about the y-axis, it must satisfy Â
 so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy Â
 so there is symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
Â
-So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis
Example Question #6 : Determine The Symmetry Of An Equation
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Symmetry about the x-axis
Symmetry about the y-axis and origin
Symmetry about the y-axisÂ
Symmetry about the x-axis, y-axis, and origin
Symmetry about the x-axis, and y-axis
Symmetry about the y-axisÂ
For a function to be symmetrical about the y-axis, it must satisfy  so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy Â
 so there is not symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
Â
So there is no symmetry about the origin.
Example Question #7 : Determine The Symmetry Of An Equation
Algebraically check for symmetry with respect to the x-axis, y-axis, and the origin.Â
Symmetry about the x-axis and y-axis
Symmetry about the y-axis and the origin
Symmetry about the x-axis
Symmetry about the x-axis, y-axis, and origin
Symmetry about the y-axis
Symmetry about the y-axis
For a function to be symmetrical about the y-axis, it must satisfyÂ
 so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfyÂ
 so there is not symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the credited answer is "symmetry about the y-axis".
Example Question #8 : Determine The Symmetry Of An Equation
Which of the following best describes the symmetry of  with respect to the x-axis, y-axis, and the origin.
No symmetry
Symmetrical about the x-axis
Symmetrical about the origin
Symmetrical about the y-axis
Symmetrical about the x-axis
For a function to be symmetrical about the y-axis, it must satisfyÂ
 so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfyÂ
 so there is symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.
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