State whether the relation is a function: {(1,2), (2,4),(-3,-6), (0,0)). Then
explain why.

Step-by-step explanation:

According to the definition of a function, each input must have one output.

The input is x and the output is y. Basically, for every x there can only be one y.

The relation given is:

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

To check if it's a function, make sure each x only appears once.

The x is the first number in a point.

We see that each x (1,2,-3,0) is only listed once, so this must be a function.

Another way to check is by graphing the points and using the Vertical Line Test.

If a vertical line is drawn and crosses the function more than once at any given part of the line, it isn't a function.

The points pass the vertical line test, so this is a function.