Explain the words relation and function. Include in your explanation how the meanings of the two words differ. Give a real-word example of a relation that is not a function. Is it possible to give an example of a function that is not a relation? If so, give one. If not, explain why it is not possible.
The temperature F, in degrees Fahrenheit, that corresponds to a temperature C, in degrees Celsius, is given by the equation F = (9/5)C + 32. If you graph this equation for 0 ¡ÜC ¡Ü100, you will notice that the point whose coordinates are (45,113) is on the graph. Write a sentence that describes the meaning of this ordered pair.
The words "relation" and "function" are commonly used in mathematics to describe the relationship between two sets of data or variables. A relation is a general term used to describe any set of ordered pairs, in which each input may correspond to one or more outputs. In other words, it is a set of pairs of inputs and outputs. On the other hand, a function is a special type of relation, where each input value has a unique output value. In other words, for every input, there is exactly one output.
An example of a relation that is not a function is a mapping of students to their favorite subjects. In this case, a single student can have multiple favorite subjects, so an input (student) can have multiple outputs (favorite subjects). This violates the requirement that a function should have exactly one output for each input.
It is not possible to give an example of a function that is not a relation. This is because a function must be a relation, but with the added restriction that each input has a unique output. Since a function is a subset of a relation, all functions are relations.
In the given equation F = (9/5)C + 32, the ordered pair (45, 113) represents a temperature in degrees Celsius (C) relating to a temperature in degrees Fahrenheit (F). Specifically, it means that when the temperature is 45 degrees Celsius, it corresponds to a temperature of 113 degrees Fahrenheit according to the equation.