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Example Questions
Example Question #1 : Determine The Symmetry Of An Equation
Is the following function symmetric across the y-axis? (Is it an even function?)
Cannot be determined from the information given
Yes
This isn't even a function!
I don't know anything about this function.
No
No
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute in for
. 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.
For our function:
Thus the function is not symmetric about the y-axis.
Example Question #1 : Determine The Symmetry Of An Equation
Is the following function symmetric across the y-axis? (Is it an even function?)
I don't know!
Yes
No
There is not enough information to determine
That's not a function!
Yes
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute in for
. 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.
For our function:
Since this matches the original, our function is symmetric across the y-axis.
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 with
. Solving for
, 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 equality
Likewise if a function is even, it is symmetrical about the y-axis
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
so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy
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
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-axis
Symmetry about the x-axis, y-axis, and origin
Symmetry about the x-axis, and y-axis
Symmetry about the y-axis
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
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.
Example Question #7 : 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 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 satisfy
so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy
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 satisfy
so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy
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.
Example Question #1 : Determine The Symmetry Of An Equation
There is insufficient information to determine the answer
The given information does not include a function
No
Yes
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