Precalculus : Determine the Symmetry of an Equation

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

No

Yes

This isn't even a function!

No

Explanation:

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?) No

I don't know!

That's not a function!

There is not enough information to determine

Yes

Yes

Explanation:

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.      Explanation:

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.  