Question

Given the domain [-2,-1,0,1,2] determine the set of all possible ordered pairs and range for the relation:x+y=6 ?

Answer 1

See a solution process below:

Explanation:

To find the range we can first solve the equation for `y`:

`x + y = 6`

`x - color(red)(x) + y = 6 - color(red)(x)`

`0 + y = 6 - x`

`y = 6 - x`

Now, we can substitute each value in the domain for `x` to determine `y`;

`x = -2: y = 6 - (-2) = 6 + 2 = 8`; ordered pair is: `(-2, 8)`

`x = -1: y = 6 - (-1) = 6 + 1 = 7`; ordered pair is: `(-1, 7)`

`x = 0: y = 6 - 0 = 6`; ordered pair is: `(0, 6)`

`x = 1: y = 6 - 1 = 5`; ordered pair is: `(1, 5)`

`x = 2: y = 6 - 2 = 4`; ordered pair is: `(2, 4)`

The Range is `{8, 7, 6, 5, 4}`