Give an example of a relation in real life, and explain why it is a function.(
A real-life example of a relation that can be considered a function is the relationship between a person's height and their weight.
This relation is a function because for each given height value, there is only one corresponding weight value. In other words, a person's weight is uniquely determined by their height. For example, if someone is 5 feet 6 inches tall (a specific height value), then their weight can be determined precisely, such as 150 pounds (a unique weight value).
This function property holds true since the height of a person does not result in multiple weight values. If it did, it would violate the function condition because for the function to be valid, each input (height) should correspond to exactly one output (weight). However, there can be multiple people with the same height but different weights, which is perfectly valid for a function.
An example of a relation in real life that is a function is the relation between a person's age and their height. In this relation, age is the input (independent variable), and height is the output (dependent variable).
This relation is a function because for each specific age, there is only one corresponding height. For example, if we consider a person who is 10 years old, there is a unique height associated with that age. The height of the person may change as they get older, but at any given age, there is only one height value. This characteristic of having a unique output for every input is what makes the relation a function.
One example of a relation in real life that can be considered a function is the relationship between a person's height and their weight. This relation is a function because for every individual, their height corresponds to a unique weight.
To understand why this relation is a function, we can examine the definition of a function. A function is a set of ordered pairs, where each input (or x-value) is paired with a unique output (or y-value). In our example, the input is a person's height and the output is their weight.
For any given height, there will be a specific weight associated with it. No two individuals of the same height would have the exact same weight. This means that each input (height) is matched with only one output (weight), satisfying the condition of uniqueness.
Consequently, we can conclude that the relationship between height and weight is a function because it meets the criteria for a function: each input (height) is uniquely associated with an output (weight).