To determine whether the relation shown in the mapping diagram is a function, let's analyze the diagram:

A relation is a function if every input (from the first set, in this case, "Age in years") maps to exactly one output (from the second set, in this case, "Height in meters"). This means that each value in the domain (age) should correspond to only one value in the range (height).

Observations:

1. Age 14 maps to 1.64.
2. Age 15 maps to both 1.68 and 1.71.
3. Age 16 maps to 1.71.
4. Age 17 maps to 1.72.
5. Age 18 maps to 1.73.

Since age 15 is associated with two different heights (1.68 and 1.71), the relation violates the definition of a function. Each input must map to exactly one output for the relation to be a function.

Conclusion:

The correct option is Option #2: The relation is not a function.

Would you like me to provide further explanation or visual aids? Let me know if you have additional questions.

Here are 5 related questions to deepen your understanding:

1. What are some real-world examples of relations that are not functions?
2. How can we visually identify if a relation is a function in other representations, like graphs?
3. What would the mapping diagram look like if the relation were a function?
4. Can a function have the same output (range value) for multiple inputs? Why?
5. What is the importance of the domain and range in determining functions?

Tip: Always check if every input corresponds to exactly one output when deciding if a relation is a function!