Select all the relations that are functions (Hint: 3 correct answers).
Question 5 options:
{(2, 2),(4, 4),(6, 6),(8, 8)}
{(0, 3),(3, 5),(5, 6),(8, 4)}
{(1, 2),(3, 3),(4, 8),(6, 3)}
{(3, 4),(5, 2),(5, 6),(7, 3)}
The relations that are functions are:
{(2, 2),(4, 4),(6, 6),(8, 8)}
{(0, 3),(3, 5),(5, 6),(8, 4)}
{(1, 2),(3, 3),(4, 8),(6, 3)}
To determine which relations are functions, we need to check if each input value (x) is associated with only one output value (y). Let's examine each option:
Option 1: {(2, 2),(4, 4),(6, 6),(8, 8)}
- In this relation, each input x is associated with only one output y. It is a function.
Option 2: {(0, 3),(3, 5),(5, 6),(8, 4)}
- In this relation, each input x is associated with only one output y. It is a function.
Option 3: {(1, 2),(3, 3),(4, 8),(6, 3)}
- In this relation, the input value 3 is associated with two different output values (3 and 8). It is not a function.
Option 4: {(3, 4),(5, 2),(5, 6),(7, 3)}
- In this relation, the input value 5 is associated with two different output values (2 and 6). It is not a function.
Therefore, the correct options are options 1 and 2.
To determine which relations are functions, we need to check if there is a unique output value for each input value.
Let's analyze each option:
1. {(2, 2), (4, 4), (6, 6), (8, 8)}: This relation has a unique output value for each input value. For example, when the input is 2, the output is 2. Similarly, for input values 4, 6, and 8, the output values are also the same. So, this relation is a function.
2. {(0, 3), (3, 5), (5, 6), (8, 4)}: This relation also has a unique output value for each input value. For example, when the input is 0, the output is 3. Similarly, for input values 3, 5, and 8, the output values are also unique. So, this relation is a function.
3. {(1, 2), (3, 3), (4, 8), (6, 3)}: This relation does not have a unique output value for each input value. When the input is 3, the output can be either 3 or 8. So, this relation is not a function.
4. {(3, 4), (5, 2), (5, 6), (7, 3)}: This relation also does not have a unique output value for each input value. When the input is 5, the output can be either 2 or 6. So, this relation is not a function.
Therefore, the relations that are functions are the first two options:
{(2, 2), (4, 4), (6, 6), (8, 8)} and {(0, 3), (3, 5), (5, 6), (8, 4)}.