Precalculus : Determine the Symmetry of an Equation

Study concepts, example questions & explanations for Precalculus

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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?) 

 

Possible Answers:

I don't know anything about this function. 

No

This isn't even a function! 

Yes 

Cannot be determined from the information given 

Correct answer:

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 #2 : Determine The Symmetry Of An Equation

Is the following function symmetric across the y-axis? (Is it an even function?) 

Possible Answers:

Yes 

I don't know! 

No 

That's not a function! 

There is not enough information to determine

Correct answer:

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.

Possible Answers:

Correct 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.

The correct answer is:

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