to figure out if a graph is a function, you can use this thing called the vertical line test. in case you're unfamiliar, it's basically where you just imagine a vertical line going from left to right on the graph. if it crosses the function in two places, it's incorrect. i suggest looking up a video that shows you a visual representation of the vertical line test if you've never heard of it; it's fairly simple.
A is a function because the graph passes the vertical line test. if you imagine a vertical line and drag it from left to right across the graph, the linear function graphed in choice A does not have two x values at the same spot.
B is not a function. it fails the vertical line test almost immediately: the sideways "U" shapes makes it intersect the vertical line twice in one place.
C is a function. it passes the vertical line test, even though it looks a little strange. at no point does it intersect the vertical line twice.
D is a function. again, it doesn't intersect the vertical line twice.
now, to determine if a function is a one-to-one function, it must also pass the horizontal line test. this means that it doesn't intersect at two points horizontally as well. test that out on choices A, C, and D.
A is a one-to-one function because it doesn't cross in the same place horizontally, either. C and D are one-to-one functions as well.
