1-to-1 means that given f(x), if f(a)=f(b) if and only if a=b. That's just saying that any y-value must have only one x-value. If you have two points on the graph like (1,5) and (2,5) then the graph isn't of a one-to-one function. An easy way to test this graphically is to look at all horizontal lines that could intersect the graph. If a horizontal line can touch the graph at two points, it's not one-to-one.

See here for a better description: Horizontal line test - Wikipedia, the free encyclopedia

Without using graphs, look for things like even functions, trig expressions that contain an x, absolute value signs, etc. Things like (x)^2 make -x and x the have the same output and graphs that repeat the same path over and over again like sin(x) won't work as well.