Question

How do you know this is a function: (-2,10) (4,1) (9,-4) (3,2) (0,-9)?

Answer 1

The given points all have different x-coordinates.

Explanation:

Recall that a function is a relationship where an inputted number gives only one output number. If there are two or more outputs for a given input, the relationship does not represent a function.

In your case, since each x-coordinate in the given points has only one y-coordinate, these points would represent a function.

However, if there was an added point that had an x-coordinate of any of the given points, the relationship would not represent a function since there would be two points with the `color(red)("same x-coordinate")` but `color(green)("different y-coordinate")`.

For example:

• represents a function
  `(1,5),(4,3),(-3,2)`

• does not represent a function
  `(color(red)1,color(green)5),(4,3),(color(red)1,color(green)7)`