Let's go through the four answer choices to see which are a function, and which aren't.
(A) This is a function since the x coordinates of the points are -6, 4, 1, 8; none of which repeat. Each x input leads to exactly one and only one y output.
(B) The same idea happens as it did with (A). The x coordinates are 3, -7, -2, 0 and none of those repeat. Therefore this is a function.
(C) Like with the others, none of the x coordinates repeat. We have another function.
(D) Unlike the others, x = -2 repeats itself twice. We have the point (-2,4) and (-2,5). This tells us the input x = -2 leads to simultaneous outputs of y = 4 and y = 5. This isn't allowed in a function (see part (A) above). Therefore, relation D is <u>not</u> a function.
If you wanted, you can use the vertical line test as a visual tool to check if we have a function or not. Graphs (A) through (C) will pass the vertical line test. Meanwhile graph D does not pass the vertical line test because of the points (-2,4) and (-2,5) mentioned earlier. You can use graphing tools like GeoGebra or Desmos.
