Explanation:
(2,4),(3,5),(4,6),(5,8) (1,4),(2,3),(3,-6),(-3,6)
is NOT a function, because some x values (2 and 3) have more than one associated result value (4, 3 and 5, -6).
(1,5),(1,7),(1,-5),(1,-7) (0,4),(1,4),(2,4),(3,4)
is NOT a function as the x value 1 has more than 1 associated result values (5, 7, -5, -7, 4).
x² = y + 1
y = x² - 1
this is a function. for any value of x we get exactly one result value.
xy = 1
y = 1/x
this is a function. for any value of x we get exactly one result value. but we do need to exclude x=0.
if we cannot do that, then it is NOT a function, because x=0 has no associated result value.
x = 3
is NOT a function, because although there is only one valid x value (3), there are infinitely many possible y result values associated with this x value (y can be "anything").
y = -2
this is a function. for any value of x we get exactly one result value (constantly -2).