Which of the following relations is a function? {(-3, 1), (0,1), (2, 5)}, {(2,-3),(2,0),(2,5)}, {(-2, -2), (0,0),(0,-2)}, or {(1,-3), (0,-1), (3,2), (1,0)}

Answer 1

For a set of points to be a function, each x can only be paired with one y value. In the first set of points, each x value only has one y value so this is a function. In the second set of points, the x point 2 has two different y values so this is not a function. In the third set of points, the x value 0 had two y values so this is not a function. In the fourth set of points, the x value 1 has two different y values so this is also not a function. The first set of points is the only function.

Answer 2

only the first is a function,

2nd, 3rd,and 4th are not functions

if you plot them on a graph, and you have one point directly above the other, it's not a function.

It's called the "vertical line" test. If you can draw a vertical line that intersects more than one point, it's not a function.

Answer 3

Think of a relation as a soda machine.

When you press a button (your x-value), you always get the same brand of soda. That button always gives you the same thing. To be a good soda machine, that button can only give you that type of soda.

A Relation is like that: for any x there is only 1 y-value.

Now the machine can have more than one button (your x-value) that gives you the same soda.

You can use more than one button (x) to get the same soda (y).

You can have more than one x-value result in the same y-value.

Example: X² = Y. If X = 2 it ALWAYS equals 4. If X = -2, also ALWAYS equals 4.

To figure if you have a relation, look to see if you have the same x-value in more than 1 set of coordinates BUT has 2 different y-values. If there is more than one set with duplicate X's and 2 different Y's, its NOT a relation; its a rotten soda machine.