Question

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

Answer 1

The relation given by the points (-3,-1), (-2,0), (-1,3), (-1,0), (0,-1) is not a function because the x-value -1 maps to two different y-values.

Step-by-step explanation:

To determine whether the given set of points defines a function, we need to look at the x-values. By definition, for a set of points to represent a function, each x-value in the domain should map to exactly one y-value. When examining the list of points (-3,-1), (-2,0), (-1,3), (-1,0), (0,-1), we notice that the x-value -1 is associated with two different y-values (3 and 0). This duplication of the x-value with different corresponding y-values violates the definition of a function.

Therefore, the relation is not a function because the x-value -1 is mapped to two different y-values, which fails the vertical line test for functions.

A relation is a function if each input (x-value) is paired with exactly one output (y-value). In this case, the relation (-3,-1) (-2,0) (-1,3) (-1,0) (0,-1) is not a function because the input value -1 is paired with two different output values: 3 and 0. A function cannot have multiple outputs for the same input.

Answer 2

no

Step-by-step explanation:

No, the given set of ordered pairs {(-3, -1), (-2, 0), (-1, 3), (-1, 0), (0, -1)} 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 -1 is associated with both y = 3 and y = 0. Therefore, the relation is not a function.