Question

How do you find the domain and the range of the relation, and state whether or not the relation is a function {(4, –6), (3, –6), (–2, 5), (4, 1)}?

Answer 1

Domain : `-{2, 3, 4}`

Range : `{-6, 1, 5}`

Not a function.

Explanation:

The domain is also known as the `x`-values and the range is the `y`-values.

Since we know that a coordinate is written in the form `(x, y)`, all the `x`-values are:
`{4, 3, -2, 4}`

However, when we write a domain, we typically put the values from least to greatest and do not repeat numbers. Therefore, the domain is:
`-{2, 3, 4}`

All the `y`-values are:
`{-6, -6, 5, 1}`

Again, put them in least to greatest and do not repeat numbers:
`{-6, 1, 5}`

In a function, each `x-`value can only pair with one `y`-value (each input has a single output). Since there are two "`4`"s in the `x`-values, there are two same `x`-values paired with two different `y`-values, so this relation is not a function.

Hope this helps!