Is a graph symmetric to the x-axis always, sometimes, or never a function? !

Alright! So, your answer is: never a function.

First thing first, let's visualize what a graph symmetric to the x-axis looks like.

Take a look at the first attachment.

Pretty clear, it's symmetric across the x-axis.

To figure out if something is a function or not, use the vertical line test! What you do, is run a vertical line down the graph. Does it eventually give you more than one point? Then it's not a function.

Take a look at this the second attachment.

The vertical line intercepts in 3 different points at once on the top picture. Therefore, it is not a function.

If you're ever uncertain, try the vertical line test. :>

I haven't used in a long while, so pardon if the attachments are a little wonky.

combine all like terms then its just a 2 step equation