Give an example of a relation in real life, and explain why it is a function.
One example of a relation in real life that is a function is the relation between a student and their assigned student ID number in a school.
In this example, every student in the school is assigned a unique student ID number. Each student has only one ID number, and there is no student who shares the same ID number with another student. Therefore, for every student, there is exactly one corresponding student ID number assigned to them.
This relation satisfies the criteria of a function because it is a set of ordered pairs, where each student is paired with their corresponding student ID number. It is also a function because each student is associated with exactly one student ID number, and no student is associated with more than one ID number. Moreover, there is no student in the school who does not have an assigned student ID number, ensuring that the relation is a total function.
An example of a relation in real life that is a function is the relationship between a person's age and their height.
In this example, the input variable is the age of the person, and the output variable is their height. For each age, there is only one corresponding height, making it a function.
This relation is a function because each person has a unique age and corresponding height at any given time. As a person grows older, their height tends to increase, but at any given age, there is only one possible height. Therefore, there is a distinct output (height) for every input (age), satisfying the definition of a function.
An example of a relation in real life that can also be considered a function is the relationship between a person's age and their height. The function would be: f(age) = height.
To understand why this is a function, we need to determine if there is a unique height corresponding to each age. In general, as a person gets older, they tend to grow taller. However, there may be some exceptions due to other factors such as genetics, health issues, or growth spurts.
To establish whether it is a function, we need to ensure that for each value of age, there is only one corresponding value of height. This means that each age should map to one specific height without any ambiguity or multiple answers. In the context of the example, assuming we are considering the average growth pattern of healthy individuals, as a person grows older, they will not shrink in height. Therefore, for each age, there will only be one specific height value associated with it, satisfying the criteria of a function.
However, it's important to note that the real-life relationship between age and height may not be a perfect function for everyone, as individual factors can influence growth. Nevertheless, in general, this example demonstrates why the relationship between a person's age and height can be considered a function.