Question

Which ordered pair can be removed so that the resulting graph represents a function?

a. (–2, 2)
b. (1, 3)
c. (5, –4)
d. (–4, –4)

Answer 1

The correct option is b.

Explanation:

Graph represents a relation and the coordinates of each points are,

`R=\{(-5,-3),(-4,-4),(-2,2),(1,-2),(1,3),(2,1),(5,-4)\}`

A relation is called function if there exist a unique value of y for each value of x.

It the above relation for each value of a x there exist a unique y except (1,-2) and (1,3). If one of these point is removed, then the resulting graph represents a function.

Therefore correct option is b.

Answer 2

(1, 3) can be removed so that the resulting graph represents a function.

Solution-

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y.

Here,

X = {-5, -4, -2, 1, 2, 5}

Y = {-4, -3, -2, 1, 2, 3}

Relation from X to Y : {(-5, -3), (-4, -4), (-2, 2), (1, -2), (1, 3), (2, 1), (5, -4)}

This relation is not a function from X to Y because the element 1 in X is related to two different elements, -2 and 3

So, we have to remove either (1, -2) or (1, 3) in order to make this a function.