#### Answer

Domain: {4, -2, 3}
Range: {-2, 4, -8, 5}
This relation is not a function.

#### Work Step by Step

The question asks us to find the domain, range and to determine if the relation given to us is a function. A relation is a set of ordered pairs.The relation given is
{ (4,-2),(-2,4),(3,-8),(4,5) }
In order to find the domain and range, you look at x and y.
$(x,y)$
Our x is the first number and our y will be the second number. From this, we can see our domain (x) are
{ 4,-2, 3 }
Even though 4 is repeated, we only have to list it once in our domain.
Now we look at all the y points to make up our range.
{-2, 4, -8, 5}
In order to check if this qualifies as a function, we must check to see if each x point has a corresponding y point. X points can have the same shared y point. However, a y point can never share two of the same x points. In this instance, the x point 4 is shared with -2 and 5. Because of this, the relation is not a function. An x point cannot be repeated.