“Functions are mathematical ideas that take one or more variables and produce a variable. You can think of a function as a cook that takes one or more ingredients and cooks them up to make a dish. Depending on what you put in, you can get very different things out”. (Function basics, n.d., para.1). In an abstract Mathematical sense, a function is a mapping of some domain onto some range. For each item in the domain, there is a corresponding item in the range of the function” (Function basics, n.d., para.2).
Several types of functions exist such as linear, quadratic, cubic, composite, even and odd, monotonic, periodic, and so on. All these functions could be related to some activity that we come across in our daily life. Let’s consider some areas which have the form of a linear function. “Mathematical equation in which no independent variable is raised to a power greater than one. A simple linear function with only one independent variable (y = a + bx) traces a straight line when plotted on a graph. Also called linear equation” (Linear function: Definition, 2009).
Consider the situation where one gets pocket money M every day and suppose he spends this money only on phone calls. Assuming $2 be the call rate per minute and suppose the person talks T minutes daily, we can represent the person’s daily balance with the following linear equation F = M – (2 × T) Where F gives the balance. Looking at the equation, one can deduce that the function daily balance depends on two variables, and hence it is called a linear equation in two variables.
The higher the minutes of the call, the lesser would be the balance left at the end of the day. Assume that the same person does a part-time job as an academic writer where he gets paid by the number of pages he writes ($3 per page). If he writes P number of pages daily, then his daily income would be 3×P. Adding this to his daily balance we get his daily actual balance to be Factual = (3×P) + M – (2×T). This equation represents the actual balance to be a function of three variables and hence it is called a linear equation in three variables.
Let us take a different situation where a person runs several miles. The distance he runs depends on the time and speed at which he runs. Assume that the person always runs at S m/sec then the distance that the person covers would be the function F(x) = S × x; where x is the time he takes in seconds to cover the distance F(x). Suppose he cuts down the distance that he runs depending on the number of pushups that he takes on that day, then he will cover only S × x – T, where T is the number of pushups. If the person can break down 100 calories per meter that he runs then the total breakdown per day would be C = 100 × (S × x – T) calories.
These are some of the day-to-day events that everyone notices. Let’s explain how to frame linear equations in complex situations. Consider a tank with two pipes. One pipe A can fill the tank in 2 hrs whereas the other pipe B can empty the tank in 5 hrs. We will find the overall time required to fill the tank when both the pipes are opened. From the conditions, we find that work done by pipe A in 1 hr would be filling ½ of the tank. Similarly, pipe B empties 1/5th of the tank in 1 hr. Considering the two conditions, we can see that when both the pipes are opened effectively 3/10th of the tank is filled in 1 hr, and hence the time required to fill the tank would be 10/3 hrs ( 3hrs and 20 min). These are a few sample examples of the existence of events in the form of linear functions.
Reference List
Function basics. (n.d.). Think Quest. Web.
Linear function: Definition. (2009). Business Dictionary. Web.