Question

Select the relation that is a function.

a) {(-6, -5), (3, 2), (10, 8), (3, 3)}
b) {(-2, -1), (5, -1), (16, 3), (-3, -9)}
c) {(5, 10), (-3, 10), (-3, -10), (4, 7)}
d) {(21, 11), (21, 10), (21, 9), (21, 8)}

Answer 1

The relation that is a function is b) {(-2, -1), (5, -1), (16, 3), (-3, -9)}

Step-by-step explanation:

A relation is a function if each input value (x-value) in the relation corresponds to exactly one output value (y-value). In other words, if no two pairs in the relation have the same x-value, then it is a function. Looking at the options given:

• a) {(-6, -5), (3, 2), (10, 8), (3, 3)}
• b) {(-2, -1), (5, -1), (16, 3), (-3, -9)}
• c) {(5, 10), (-3, 10), (-3, -10), (4, 7)}
• d) {(21, 11), (21, 10), (21, 9), (21, 8)}

Option a) is not a function because it has two pairs with the same x-value of 3. Option b) is a function because each x-value is paired with a unique y-value. Option c) is not a function because it has two pairs with the same x-value of -3. Option d) is not a function because all the pairs have the same x-value of 21.

Therefore, the relation that is a function is b) {(-2, -1), (5, -1), (16, 3), (-3, -9)}.