Determining which functions are one to one 
So I know for sure that $x^3$ is one to one, being that the entire span of real number $y$'s can be found by some x and it passes the vertical line test. Graphically, its pretty clear. I know that $x^2$ is also one to one though not onto, since no negative $y$'s can be obtained. I don't have the same graphical intuition for options B, D, and E. How would I go about making that determiniation? 

The easiest way is to look at the kernel for the not-so obvious ones. I should note that this works for only linear maps. 
(b) The kernel is $\{ (x,x,x) \}$, so no not injective
(c) No, clearly.
(d) The kernel of this is $\{(x,-x) \}$, so no not injecive
(e) Yes the kernel of this is trivial (can you see why?)
