Take The Quiz To Learn About Relations & Functions

1. Which of the following is not a function?

{(0,2), (1,3), (4,3), (1,2)}

{(0,1), (1,2), (2,3), (3,4)}

{(1,3), (4,2), (2,0), (3,4)}

{(1,2), (2,2), (3,2), (4,2)}

A function is a relation where each input has exactly one output. In the given answer, the set {(0,2), (1,3), (4,3), (1,2)} violates this property because the input value 1 is associated with two different output values, 3 and 2. Therefore, this set is not a function.

Explanation

A function is a relation where each input has exactly one output. In the given answer, the set {(0,2), (1,3), (4,3), (1,2)} violates this property because the input value 1 is associated with two different output values, 3 and 2. Therefore, this set is not a function.

2. {(7, 1), (7, -3), (7, 4)}

Function

Not a Function

Both

Neither

The given set of points {(7, 1), (7, -3), (7, 4)} does not represent a function because for a set of points to represent a function, each x-coordinate should have only one corresponding y-coordinate. In this case, the x-coordinate 7 has three different y-coordinates (-3, 1, and 4), which violates the definition of a function. Therefore, the correct answer is "Not a Function".

Explanation

The given set of points {(7, 1), (7, -3), (7, 4)} does not represent a function because for a set of points to represent a function, each x-coordinate should have only one corresponding y-coordinate. In this case, the x-coordinate 7 has three different y-coordinates (-3, 1, and 4), which violates the definition of a function. Therefore, the correct answer is "Not a Function".

3. { (-3, 2), (-2, 1), (-1, 0), (0, 1), (1, 2), (2, 3)}

Function

Not a Function

Both

Neither

The given set of ordered pairs represents a function because each input value (x) is associated with only one output value (y). In other words, for each x-value, there is only one y-value. Therefore, the set of ordered pairs represents a function.

Explanation

The given set of ordered pairs represents a function because each input value (x) is associated with only one output value (y). In other words, for each x-value, there is only one y-value. Therefore, the set of ordered pairs represents a function.

4. Which of the following relation is not a function?

{(2,7), (3,7), (4,7), (5,8)}

{(3,-2), (5,-6), (7,7), (8,8)}

{(1,-5), (-1,6), (1,5), (6,-3)}

{(1,-5), (3,1), (-5,4), (4,-2)}

In a function, each input value (x) can only have one corresponding output value (y). However, in the given relation {(1,-5), (-1,6), (1,5), (6,-3)}, the input value 1 has two different output values (-5 and 5). Therefore, this relation is not a function.

Explanation

In a function, each input value (x) can only have one corresponding output value (y). However, in the given relation {(1,-5), (-1,6), (1,5), (6,-3)}, the input value 1 has two different output values (-5 and 5). Therefore, this relation is not a function.

5.

Function

Not a Function

Both

Neither

not-available-via-ai

Explanation

not-available-via-ai

6. {(6, -3), (7, 4), (-7, -2), (0, -2)}

Function

Not a Function

Both

Neither

The given set of points {(6, -3), (7, 4), (-7, -2), (0, -2)} represents a function. In a function, each input (x-value) is associated with exactly one output (y-value). In this case, for every x-value, there is only one corresponding y-value. Therefore, it satisfies the definition of a function.

Explanation

The given set of points {(6, -3), (7, 4), (-7, -2), (0, -2)} represents a function. In a function, each input (x-value) is associated with exactly one output (y-value). In this case, for every x-value, there is only one corresponding y-value. Therefore, it satisfies the definition of a function.

7.

Function

Not a Function

Both

Neither

not-available-via-ai

Explanation

not-available-via-ai

8.

Function

Not a Function

Both

Neither

not-available-via-ai

Explanation

not-available-via-ai

9. What is y = x + 3?

Relation

Function

Both

Neither

The equation y = x + 3 represents a linear relationship between x and y, where y is always equal to x plus 3. This equation satisfies the definition of a function because for every input value of x, there is exactly one corresponding output value of y. Therefore, the correct answer is "Function."

Explanation

The equation y = x + 3 represents a linear relationship between x and y, where y is always equal to x plus 3. This equation satisfies the definition of a function because for every input value of x, there is exactly one corresponding output value of y. Therefore, the correct answer is "Function."

10. What is A = {9, 16, 25} and B = {5, 4, 3, -3, -4, -5}?

Relation

Function

Both

Neither

The given sets A = {9, 16, 25} and B = {5, 4, 3, -3, -4, -5} represent a function because each element in set A maps uniquely to an element in set B. Specifically, each element in set A, which consists of perfect squares, maps to its square root in set B. Therefore, it forms a function from A to B.

Explanation

The given sets A = {9, 16, 25} and B = {5, 4, 3, -3, -4, -5} represent a function because each element in set A maps uniquely to an element in set B. Specifically, each element in set A, which consists of perfect squares, maps to its square root in set B. Therefore, it forms a function from A to B.