Question

The tables below represent two different relations between the variables x and y. Which relation is a function and which is not a function?

Table 1:

x 0 -4 3 -2 9 3
y 5 8 7 8 5 -2

function or not function?

Table 2:

x 2 -7 5 1 -6 3
y 5 8 -6 8 5 7

function or not function?

Which ordered pair can be omitted from the non-function so that the relation is a function?

Answer 1

Table 1: Not a function.

Table 2: It is a function.

Explanation:

A relation is a function if each x value is mapped to a single y-value.

i.e. corresponding to each element there is a single image.

Table 1:

x 0 -4 3 -2 9 3

y 5 8 7 8 5 -2

No, Table 1 is not a function.

Since there are two images of element '3'.

i.e. 3 is mapped to 7 and -2.

Table 2:

x 2 -7 5 1 -6 3

y 5 8 -6 8 5 7

Yes, this relation is a function.

Because corresponding to each x there is a single image.

If from Table 1 we delete the ordered pair either one of (3,7) or (3,-2) we will obtain the relation as a function.

Answer 2

table 1: not a function
table 2: function

3,-2