Graph H: This hyperbola is symmetric about the lines y = x and y = –x, but this tells me nothing about evenness or oddness. However, the graph is also symmetric about the origin, so this function is odd.

How do you determine if a function is odd or even?

You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.

Is a radical function even or odd?

So, to find the domain of a radical function with even index, we set the radicand to be greater than or equal to zero. For an odd index radical, the radicand can be any real number. When the index of the radical is even, the radicand must be greater than or equal to zero.