Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
Answers
SOLUTION
TO CHOOSE THE CORRECT OPTION
Which set of ordered pairs represents a function
- {(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
- {(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
- {(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
- {(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
CONCEPT TO BE IMPLEMENTED
Function :
Let A and B are two non empty sets. A mappings or function f from A to B is a rule that assigns to each element x of A a definite element y in B
EVALUATION
First we rename the relations
f = {(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
g = {(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
h = {(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
p = {(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
Let in each case domain = A and range = B
(i) f is not a function since the element 1 in A is related to two different element ( 5 & - 3 ) of B by the relation
(ii) g is a function since g assigns to each element x of A a definite element y in B
(iii) h is not a function since the element - 2 in A is related to two different element ( - 5 & 9 ) of B by the relation
(iv) p is not a function since the element - 3 in A is related to three different element ( 1 , 2 & - 3 ) of B by the relation
FINAL ANSWER
Hence the correct option is
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
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