Question

Which relation is a function? {(–4, –6), (–3, –2), (1, –2), (1, 0)} {(–2, –12), (–2, 0), (–2, 4), (–2, 11)} {(0,1), (0, 2), (1, 2), (1, 3)} {(8, 1), (4, 1), (0,1), (–15, 1)}

Answer 1

`\{(8, 1), (4, 1), (0,1), (-15, 1)\}`

Explanation:

Given

`\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}`

`\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}`

`\{(0,1), (0, 2), (1, 2), (1, 3)\}`

`\{(8, 1), (4, 1), (0,1), (-15, 1)\}`

Required

Determine which is a function

A relation is divided into 2; (x,y)

Where x represents the range and y stands for the domain

For a relation to be a function, the x column must be unique; in other words, there must be only one occurrence of x

Testing each of the given options

A.
`\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}`

Start by splitting the relation into x and y columns

`(x,y)`

`(-4, -6)`

`(-3, -2)`

`(1, -2)`

`(1, 0)`

Notice that the third and fourth relation has the same x value of 1;

Hence, this is not a function

B.
`\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}`

Start by splitting the relation into x and y columns

`(x,y)`

`(-2, -12)`

`(-2, 0)`

`(-2, 4)`

`(-2, 11)`

Notice that all relations has the same x value of -2;

Hence, this is also not a function

C.
`\{(0,1), (0, 2), (1, 2), (1, 3)\}`

Start by splitting the relation into x and y columns

`(x,y)`

`(0, 1)`

`(0, 2)`

`(1, 2)`

`(1, 3)`

Notice that the first and second relation has the same x value of 0 and the third and fourth relation has the same x value of 1;

Hence, this is also not a function

D.
`\{(8, 1), (4, 1), (0,1), (-15, 1)\}`

Start by splitting the relation into x and y columns

`(x,y)`

`(8, 1)`

`(4, 1)`

`(0, 1)`

`(-15, 1)`

Notice that relation has the unique x values of 8, 4, 0 and -15

Hence, this relation is a function