Question

How many points need to be removed from this graph so that it will be a function?

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

From the given graph it is noticed that the coordinates of all the points are (-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4).

So, the graph represents a relation,

R = {(-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4)}

A relation is called a function if an only if for each value of x there exist a unique value of y.

In the given relation, for each value of x we have two values of y. So it is not a function. We need to remove any of ordered pairs that have same input values.

From (-3,2) and (-3,3), we need to remove one point.

From (1,4) and (1,-4), we need to remove one point.

From (2,-2) and (2,-4), we need to remove one point.

It means total we need to remove 3 points from this graph so that it will be a function.

Therefore the correct option is 3.

Answer 2

In a function, you cannot have more than one point with any x-coordinate.
There are two sets of points that cause problems.
(-2, 2) and (-2, 3) have the same x-coordinate, -2.
(2, -2) and (2, -4) have the same x-coordinate, 2.
If you remove one of the points with x-coordinate -2 and one of the points with x-coordinate 2, then you'd have a function, so the answer is 2.