determine if the given relation is function or not based on given domain and range

Question

example:

{(1,5),(2,6),(3,7),(4,8)}

Answer 1

When these points are plotted they all lie on a straight line. Even without plotting them you can see there's a simple connection between one point and the next, since we have two simple number sequences for x and y. x goes up on steps of 1 and so does y. The function is the standard straight line function y=ax+b. When x=1, y=5, when x=2, y=6, and so on. Substituting these values we get 5=a+b and 6=2a+b. Subtract the first equation from the second and we get the b's cancelling out and we're left with a=1. If we put a=1 into either equation we get b=4, so the function y=x+4, a straight line with positive slope (/). The domain is the range of values of x for which the function is defined, that's between 1 and 4, and the range of the function between 5 and 8.