IM1 6.1 Relations and Functions

Which graph represents a function?

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Which of the relations below is a function?

• {(2, 3), (3, 4), (5, 1), (2, 4)}

• {(2, 3), (3, 4), (6, 2), (7, 3)}

• {(2, 3), ( 3, 4), (6, 2), (3, 3)}

Answer explanation

A function must have unique outputs for each input. The relation {(2, 3), (3, 4), (6, 2), (7, 3)} has unique first elements (inputs), making it a function. The other options have repeated inputs.

The graph of a relation is shown at the right. Is this relation a function?

• Yes

• No

• Cannot be determined from a graph

Answer explanation

A relation is a function if each input has exactly one output. If the graph shows any vertical line intersecting it at more than one point, it indicates that a single input corresponds to multiple outputs. Therefore, this relation is not a function.

The graph of a relation is shown below. Is the relation a function?

• Yes

• No

• Cannot be determined from a graph

Answer explanation

Yes, the relation is a function because each input (x-value) corresponds to exactly one output (y-value). This is confirmed by the vertical line test, where no vertical line intersects the graph at more than one point.

Is the relation depicted in the table below a function?

• Yes

• No

• Cannot be determined from a table

Answer explanation

Yes, the relation is a function because each input (x-value) corresponds to exactly one output (y-value). There are no repeated x-values in the table, confirming it meets the definition of a function.

• Function
• Not a Function

Does the graph represent a function?

• Yes, because the vertical line test shows there are no repeating input values

• No, because the vertical line test shows there are repeating input values

Answer explanation

No, because the vertical line test shows there are repeating input values. This indicates that for at least one input, there are multiple outputs, which violates the definition of a function.

Is this a function? 

• Yes 

• No

Answer explanation

Yes, this is a function because it assigns exactly one output for each input, satisfying the definition of a function in mathematics.

List the ordered pairs

• (1,3), (2,6), (3,9), (4,12)

• (3,1), (6,2), (9,3), (12,4)

• Input and Output

• Output and Input

Answer explanation

The correct ordered pairs are (1,3), (2,6), (3,9), (4,12) because they follow the pattern of multiplying the first element by 3 to get the second element. The other option reverses this relationship.

Is the relation a function?

• Yes, each input has one output

• No, each input has more than one output

• No, the cost of the movies is different

• Yes, each output has one input

Answer explanation

The correct answer is 'Yes, each input has one output' because a function is defined as a relation where each input corresponds to exactly one output, ensuring no input has multiple outputs.