Choose if the following relations are functions or not functions.
{(4,-8), (2,-8), (-8,-8), (0,-8)} is
{(3,9), (-3,1), (5,3), (3,3), (10,14)} is
{(7,2), (8,-1.4), (4.5,-10), (7,2), (1.2,1.8)} is
{(0,0), (1,1), (2,2), (3,3), (4,4)} is
The first relation is a function because each input (x-value) is paired with only one output (y-value).
The second relation is not a function because the input value 3 is paired with both 9 and 3.
The third relation is not a function because the input value 7 is paired with both 2 and 2.
The fourth relation is a function because each input (x-value) is paired with only one output (y-value).
The given relations can be classified as functions or not functions using the definition of a function, which states that for every input (or x-value), there must be a unique output (or y-value). Let's analyze each relation:
1. {(4,-8), (2,-8), (-8,-8), (0,-8)}:
This relation is a function because each x-value has a unique y-value. In this case, all the x-values are different, but the y-values are all the same (-8). Therefore, it satisfies the definition of a function.
2. {(3,9), (-3,1), (5,3), (3,3), (10,14)}:
This relation is not a function because there is a repeated x-value. The input value 3 has two different output values (9 and 3), which violates the definition of a function.
3. {(7,2), (8,-1.4), (4.5,-10), (7,2), (1.2,1.8)}:
This relation is not a function because there is a repeated x-value. The input value 7 has two different output values (2 and 2), which violates the definition of a function.
4. {(0,0), (1,1), (2,2), (3,3), (4,4)}:
This relation is a function because each x-value has a unique y-value. In this case, the x-values are the same as the y-values, demonstrating a one-to-one correspondence between inputs and outputs, satisfying the definition of a function.
To determine if a relation is a function or not, you need to check if each input value (x-coordinate) in the relation is associated with a unique output value (y-coordinate).
Let's analyze each given relation:
1) {(4,-8), (2,-8), (-8,-8), (0,-8)}
Since all the input values (x-coordinates) are associated with the same output value (-8), this relation is a function.
2) {(3,9), (-3,1), (5,3), (3,3), (10,14)}
In this relation, the input value 3 is associated with two different output values (9 and 3). Therefore, this relation is not a function.
3) {(7,2), (8,-1.4), (4.5,-10), (7,2), (1.2,1.8)}
Here, the input value 7 is associated with two different output values (2 and 2). Thus, this relation is not a function.
4) {(0,0), (1,1), (2,2), (3,3), (4,4)}
In this relation, each input value (x-coordinate) is associated with a unique output value (y-coordinate). Therefore, this relation is a function.
To summarize:
1) Function
2) Not a function
3) Not a function
4) Function