In order for a relation to be a function, it has to "survive" the vertical line test. The idea is, you draw a vertical line so that it intersects the graph. Now, the line should touch the graph only ONCE. If it touches the graph at least two times - it's not a function.
The first option is a parabola laying on its side. An imaginary vertical line would touch the graph twice, so this isn't a function.
The second choice is only crossed by the imaginary line once, so it's a function.
The third choice is a linear function.
The fourth choice is a parabola, or a quadratic function.
Out of the choices provided, the first one does not pass the test.