Why is this not a function? This problem is from Discrete Mathematics and its Applications

This is the definition that the book gave of function

Here is my work so far 

It's pretty clear to me that 1b and 1c are not functions because in each case one element of R is not assigned exactly one element of R( sqrt(x) -> +sqrt(x) and -sqrt(x) ).   Why is 1a not a function though? For the ones I tried, a unique element of R was assigned to another unique element of R (4->1/4,  3-> 1/3). In the explanation, would it be possible to give each R a subscript, like you're mapping from R1 to R2? I feel like R to R is kind of confusing. I understand why the author chose not to use the subscripts though - real is the same as real

Hint: a) consider what happens at $f(0)$.
b) What happens to $f(x)$ when $x<0$?
