a)(i) Because it's f(|x|), f(x) = f(-x), so it's reflected about the y axis.
(ii)sqrt so f(x) cannot be < 0, and we only take the positive sqrt root.
(iii)Same as (ii) but we take positive and negative sqrt as it's y^2=f(x)
b)(i) y=|f(x)|, so y >= 0
(ii)Same as a)(i), reflected over y axis...