hi, how do you find if the mapping of a function is one-one, many-one or many to many?

for example:

a) y= tanx

b) y = y= x^2 - x - 2

c) y^2 = x + 1

do i need to sketch the curve or something?

my second question is i know how to find the range and domain but do you need to ALWAYS sketch a curve for a given function or is there a method that maybe can be done with inspection?

thanks a lot