Which of the following relations represent a function?
{(-1,-3),(3,2),(3,7)}
{(-3,7),(3,-7),(3,7)}
{(-1,4),(-1,7),(3,5)}
{(-1,4),(2,7),(3,7)}
{(-1,-3),(3,2),(3,7)} NO WAY, two y values for x = 3 ???
{(-3,7),(3,-7),(3,7)} SAME PROBLEM!
{(-1,4),(-1,7),(3,5)} BORING at x = -1y can not be both 4 and 7
the last one works. Y can be the same at 2 places in x
but can not be different at a particular x
Why did the function go to therapy?
Because it had multiple personalities!
Only the third relation {(-1,4),(-1,7),(3,5)} represents a function because each input (-1 and 3) is associated with only one output (4, 7, and 5 respectively).
A relation represents a function if each input has only one output. Let's analyze each relation given:
1. {(-1, -3), (3, 2), (3, 7)}
This relation is not a function because the input 3 has two outputs: 2 and 7.
2. {(-3, 7), (3, -7), (3, 7)}
This relation is not a function because the input 3 has two outputs: -7 and 7.
3. {(-1, 4), (-1, 7), (3, 5)}
This relation is not a function because the input -1 has two outputs: 4 and 7.
4. {(-1, 4), (2, 7), (3, 7)}
This relation is a function because each input has only one output: (-1, 4), (2, 7), and (3, 7).
To determine if a relation represents a function, we need to check if each input has only one corresponding output.
Let's examine each relation:
1. {(-1,-3),(3,2),(3,7)}
In this relation, the input -1 has an output of -3, the input 3 has two outputs of 2 and 7. Since 3 has multiple outputs, this relation does not represent a function.
2. {(-3,7),(3,-7),(3,7)}
In this relation, the input -3 has an output of 7, the input 3 has two outputs of -7 and 7. Again, since 3 has multiple outputs, this relation does not represent a function.
3. {(-1,4),(-1,7),(3,5)}
In this relation, the input -1 has two outputs of 4 and 7. Therefore, this relation does not represent a function.
4. {(-1,4),(2,7),(3,7)}
In this relation, each input has its own unique output. Therefore, this relation represents a function.
Only the fourth relation, {(-1,4),(2,7),(3,7)}, represents a function because each input has a single corresponding output.