Determine whether the sets are functions If a set is a funct

Determine whether the sets are functions. If a set is a function, state its domain. (a) {(3, 7), (4, 12), (-1, 8), (4, 5) Yes, it is a function. No, it is not a function. Domain: (if the set is not a function, leave this blank) {-1, 3, 4} {5, 7, 8, 12} {-1, 3, 4, 5, 7, 8, 12} {4} (b) y = -6 if x is a positive integer, and y = 6 if x is a negative integer. Yes, it is a function. No, it is not a function. Domain (if the set is not a function, leave this blank): {all positive integers} {all negative integers} {all integers except zero} {-6, 6} It is not a function.

Solution

a) { ( 3, 7 ) , ( 4,12) , ( -1 , 8 ) , ( 4,5 ) }

since all y values are unique it is a function

domain is all x values

domain is { 3,4,-1}

b)

y = -6 if x is a positive integer and y = 6 if x is a negative integer

y value is unique in both cases so

yes it is a function

domain is all integers except 0

since domain is all x values so x values can be positive or negative but not zero