What is the relation between the graphs and function and how was it applied in the real world?

Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael is first, Houston is second). The function concept is very closely connected to graphs, and functions are the heart of mathematics.

I gathered my information from books especially algebra books and some are from the internet. I went to the library to look for some books and I borrowed some so I have many resources of information.

Many real-life relations between two quantities expressed in the form of equation are functions. To visualize these relationships, geometric figures called graphs are used. Modern technology provides us with graphing utilities needed to draw these graphs as well as enhance man’s knowledge of graphing techniques. Scientist and astronomers identify, visualize, and explore graphical patterns useful in analyzing data about the universe. Economist and businessmen draw mathematical models to find curves of best fit. Generally, the use of function and graphs is found in every scientist and business activity.

Function

Function is said to be the central idea in the study of mathematics. In many situations, there is mathematical function in which one quantity corresponds to another quantity according to some definite rule.

A relation was defined as correspondence between two variables, x and y, or a set of ordered pairs (x,y) where x is related to y.

For instances, the price of a plot of land (y) is related to the number of square meters of land bought (x); the monthly wage (y) of an employee is related to the number of hours the employee worked (x); the water bill paid for the month (y) is related to the number of cubic meters of water consumed (x). In other words, the quantity or variable y depends upon the quantity or variable x.

In the third example, if the amount of water consumed for the month is known, the water bill can be predicted of water consumed then

y= basic charge (x) + other charges,

where x represents the amount of water consumed and y represent the total charge or the water bill. For instances, if the basic charge is ₱ 15.46 per cubic meter and the other charges amount to ₱ 38.39, and x is the amount of water consumed, then

y= ₱15.46 (x) + ₱38.39.

The rule above represents is function because

1. There exist a correspondence between two variables: the amount consumed (x) and the charge (y)

2. There is exactly one charge for every amount consumed.

In the definition, set X is called the domain of the function. For every element x in set X, the corresponding element y in set Y is called the value uf the function at x, or the image of x. this set of values or images of the elements of the domain is called the range of the function.

Function in the real word

In the real world, there are situation that can be represented by two variable quantities related in such a way that one variable depends upon another variable.

Examples

1. The distance covered by a car depends in how fast the car was going and on how long it has travelled.

Distance is a function of a rate and a function of times.

2. The force exerted by a 20 kg boy on a certain object depends upon his acceleration.

The force exerted by a 20 kg boy is function of his acceleration.

3. The price paid for a pizza depends on the size of the pizza.

The price of a pizza is a function of its size

4. The monthly wage a laborer earns depends upon the number or hours he worked

The monthly wage of a laborer is a function of the number...