Question

Find the domain and range and determine if it's a function or not Compare and Contrast#3

Answer 1

ANSWERS

• Domain: {-5, -4, 4, 5}

,

• Range: {-6, -5, -2, -1, 8}

,

• Function?: no

Step-by-step explanation

Domain

The domain of a function (or relation) is the set of all x-values for which the function exists.

In this case, the relation is given as a set of ordered pairs, so the domain is the set of the x-coordinates of those ordered pairs. Remember that in an ordered pair, the x-coordinate is the first number.

The x-coordinates are,

`5,-5,4,-5,-4`

To write the domain, we have to write these numbers from least to greatest, without repetition - this means that if a value is more than once, to write the domain we only write it once,

`D\colon\mleft\lbrace-5,-4,4,5\mright\rbrace`

Range

The range of a function (or relation) is the set of all the y-values.

As we did for the domain, we have to write the y-coordinates of the ordered pairs given,

`8,-2,-6,-1,-5`

And to write the range, we have to write them from least to greatest, without repetition,

`R\colon\mleft\lbrace-6,-5,-2,-1,8\mright\rbrace`

Function?

A relation is a function if there are no repeated x-values. In this problem, we can note this quickly by looking at the number of points (which is 5) and the number of values in the domain (which is 4). This happened because the x-coordinate x = -5 appears twice at different points. Therefore, because there is a repeated x-value, this relation is not a function.