Question

Can someone please explain to me why y=ln(|x|) is an odd function?

Answer 1

An odd function is symmetrical to the y-axis, but if all x-values are positive because we are finding the natural log of the absolute value of x, then the function never crosses the y-axis, therefore it can not be symmetrical, correct?

Answer 2

an odd function is symmetrical to the origin, not to the y axis. so y=ln|x| isnt odd

Answer 3

An odd function is symmetrical to the origin, the point (0, 0). It would be like the equation y = x^3. f(-x) = -f(x)

Answer 4

Ok so the function is not odd, not because it isn't symmetrical to the y-axis, but because it is not symmetrical to the origin.

Answer 5

isnt it even if its symmetric to y axis?

Answer 6

@etemplin , that is correct. Both of your posts.

Answer 7

So her function is even and it would look like: