There are x values which the function shows different y values.
For A, no x value repeats, so this must be a function.
For B, we can check graphs with the vertical line test. If we can draw a vertical line that passes through the curve more than once, the curve is not a function. But I only pass through the function once with any vertical line on the graph so this is a function.
For C, this equation is in the form of a quadratic and all quadratics are functions.
And for D, using the vertical line test I mentioned, I can draw a vertical line that passes through the graph twice, thus D is not a function.