Question: Question 7 Which relation diagram represents a function? Diagram W: - Input: 6, Output: 5…

Question 7

Which relation diagram represents a function?

Diagram W:

• Input: 6, Output: 5
• Input: -2, Output: 5
• Input: -1, Output: 5
• Input: 7, Output: 5

Diagram X:

• Input: 1, Output: -2
• Input: 1, Output: 6
• Input: 1, Output: -7
• Input: 1, Output: 4

Diagram Y:

• Input: -8, Output: 3
• Input: 9, Output: 13
• Input: 9, Output: -4
• Input: 7, Output: 0

Diagram Z:

• Input: 2, Output: 8
• Input: -7, Output: 6
• Input: 4, Output: 10
• Input: -11, Output: 9

Options:

• W.
• Z.
• X.
• Y.

Solution

A relation diagram represents a function if every input has exactly one output. Let’s analyze each option: Diagram W: - Input 6, -2, -1, 7 all map to the same output 5. - One input can map to one output. This does not violate the definition of a function. Diagram X: - Input 1 maps to outputs -2, 6, -7, 4. - A single input gives multiple outputs, so this is not a function. Diagram Y: - Input -8 maps to 3, 9 to 13, and 7 to 0. - Each input has a distinct output. This is a function. Diagram Z: - Input 4 maps to outputs 10 and 9. - A single input gives multiple outputs, so this is not a function. The correct answer is Y.