Question

Is this relation a function? If not, explain why.
(-2,-2) (2,-1) (3,0) (5,3) (5,4)

Answer 1

The given relation is not a function because the x-value of 5 is associated with two different y-values (3 and 4), failing the vertical line test.

Step-by-step explanation:

The relation given as (-2,-2) (2,-1) (3,0) (5,3) (5,4) is not a function because there are two different y-values for the same x-value (5). In a function, each x-value must correspond to exactly one y-value.

This is known as the vertical line test, where if a vertical line crosses the graph of the relation more than once, then the relation is not a function.

Since the x-value of 5 corresponds to two different y-values (3 and 4), the vertical line test fails, and therefore the relation cannot be classified as a function.

A correct example of a function is a table of points like (1,5), (2,10), (3,7), and (4,14) where each x-value has a single distinct y-value, thus showing the proper dependence of y on x.

Answer 2

no

Step-by-step explanation:

No, the given set of ordered pairs {(-2, -2), (2, -1), (3, 0), (5, 3), (5, 4)} does not represent a function. In a function, each input (x-value) should be associated with only one unique output (y-value). However, in this case, the input value 5 is associated with both y = 3 and y = 4. Therefore, the relation is not a function.