Trying to find the zeros and symmetry of f(x)= 1/(x-1)^2 +1?

Question

I put that there are no zero's and no symmetry, is that correct? I'm a little confused and wanted to double check with you guys.

Answer 1

You're correct. Since (x-1)^2 is always positive, 1/(x-1)^2 is always positive. Adding 1 to it, still makes it positive. Hence the function is never zero.

As far as symmetries go, you are also correct depending on you define symmetries. Typically, an algebra course defines the following two symmetries:

If f(-x) = f(x) you are symmetric about the y-axis.

If f(-x) = -f(x) you are symmetric about the origin.

If you use these two, then you're in the clear because neither symmetry is present. But it is symmetric about the x=1 line.

Answer 2

well, (0,2) is a zero, and there is symmetry over the line x=1

have yourself a good day.