Question

Identify ALL relations that are also functions.

A) {(6, 1), (-7, 1), (6, -7), (-9, 6)}
B) {(6, 8), (4, 9), (-5, 7), (-6, -8)}
C) {(-5, -1), (3, -10), (-1, 7), (9, 6)}
D) {(7, 5), (10, 7), (0, 3), (9, 5)}
E) {(7, 10), (-5, 1), (-2, 1), (7, -6)}

Answer 1

Out of the given relations, B), C), and D) are functions because each input maps to exactly one output. A) and E) are not functions because they have inputs that map to more than one output.

Step-by-step explanation:

To determine which of the given relations are also functions, we need to verify that for every input (x-value), there is only one output (y-value). A relation is a function if it passes the Vertical Line Test, which means that a vertical line drawn through the graph of the relation at any x-coordinate does not intersect the graph at more than one point.

• A) {(6, 1), (-7, 1), (6, -7), (-9, 6)} - This is not a function because the input '6' has two different outputs: '1' and '-7'.
• B) {(6, 8), (4, 9), (-5, 7), (-6, -8)} - This is a function because all x-values have unique y-values.
• C) {(-5, -1), (3, -10), (-1, 7), (9, 6)} - This is a function because all x-values have unique y-values.
• D) {(7, 5), (10, 7), (0, 3), (9, 5)} - This is a function because all x-values have unique y-values.
• E) {(7, 10), (-5, 1), (-2, 1), (7, -6)} - This is not a function because the input '7' has two different outputs: '10' and '-6'.