SOLUTION: Determine the symmetry (relative to the x-axis, y-axis, and/or orgin) of the graph of the following function. No need to submit graph. g(x) = 3x^2.

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Remember, a function is even when this equality is true:



and a function is odd when this equality is true:



Lets see if the function is even:

Start with the given equation
Here's :
This is the given equation
Here's :
Replace x with

Simplify
Since , this means the equation is true.

Since , the equation is an even function. This means the equation has symmetry with respect to the y axis



Now lets see if the function is odd:

Start with the given equation
Here's :
Remember we solved for this previously
Here's :
Negate the whole function

Distribute the negative and simplify
Since does not equal , this means the equation is not true.

Since does not equal , the equation is not an odd function.

When we graph the equation , we can see if the equation has any symmetry:

and we can clearly see that the equation is symmetrical with respect to the y axis
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