What does a piecewise function represent?

A piecewise function is a function where more than one formula is used to define the output over different pieces of the domain.

What is the significance of function in real life situation?

Functions are mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies and for keeping aeroplanes in the air. Functions can take input from many variables, but always give the same output, unique to that function.

How is piecewise function being used?

We use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.” For example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value.

What do you understand by the term piecewise continuous function?

A function is called piecewise continuous on an interval if the interval can be broken into a finite number of subintervals on which the function is continuous on each open subinterval (i.e. the subinterval without its endpoints) and has a finite limit at the endpoints of each subinterval.

Why is it important to learn about functions?

Functions describe situations where one quantity determines another. Because we continually make theories about dependencies between quantities in nature and society, functions are important tools in the construction of mathematical models.

How are functions used in real life?

A car’s efficiency in terms of miles per gallon of gasoline is a function. If a car typically gets 20 mpg, and if you input 10 gallons of gasoline, it will be able to travel roughly 200 miles.

What is a piecewise function consisting of a finite number of constant functions?

A piecewise continuous function is a function that is continuous except at a finite number of points in its domain.

Why is function important in real life?

Functions are mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies and for keeping airplanes in the air. Functions can take input from many variables, but always give the same output, unique to that function.