Mathematical Functions-An introduction

May 18, 2017 User 9

In this article I have explained about functions, that is very important from IB exam point of view

 functions are one of the most important areas of mathematics because they lie at the heart of much of mathematical analysis. The concept of function is easy to understand.
supposeIi say that:


where x∈R. this says that y depends on x this can be said that y is a function of x. or


we can also say that x=√y here x depends on y or x is a function in y or


so it can be said that a function is an operator which takes an input and gives an output.The input is called independent variable while output is called dependent variable

<img data-fr-image-pasted= " width="300" height="136" srcset=" 300w, 768w, 1024w, 1080w" sizes="(max-width: 300px) 100vw, 300px" >

ib elite tutor explained functions



We can also have functions with multi-dimensional outputs. that i will discuss in some other place.

Examples of function from our daily life:

1.) volume of a balloon filled with air is
                     V=4/3ΠR³   here volume depends upon the radius of the balloon so…

we can say that volume is a function of radius

2)The power dissipated by a resistor depends upon input current so we can say that power is a function of input current

3) Grades you score in your final (G) exam depends upon the hard work(H.W) input by you so we can say that grade scored is a function of hard word

if we have a function like:

                                               f(x)=x+5                  x∈N

then it means that we can input any natural number for x here.

if x=1 then F(x) or y=1+5=6 similarly we can find much output just by changing values of x.

the combination of values of x and y like (x,y)= (1,6) is called an ordered pair. this helps us to draw the graph of the function. A function can have many inputs for a sing input like

                                                 f(x)=5      x∈N

It’s ordered pairs will be like (1,5),(2,5),(3,5),(4,5),…….all these are with a single output for multiple inputs. But a function can never have more than one output for a single input. ordered pairs like (1,5),(1,6),(1,7)…..are never possible for a function



Have you thought about online lessons?

Online tuition gives you access to brilliant tutors across the country
Connect one-to-one with a tutor or share your lesson with a group for 50% of the tutor's hourly rate! Find a Tutor for One-to-One Find an Online Study Group

Want to know more?

Visit User's profile to find out more and send a message.

Visit User's Profile

Resources others found helpful

describe a celebrity

adjectives and family members

learn more


A glimpse into HTML

learn more

Dyslexia support pack for language learners

Information for students, parents & tutors which can help students to understand that their …

learn more

Intro about Dyslexia

This resource gives us a general overview of dyslexia and is a useful starting point for those who …

learn more

Free resources, revision notes and past papers for students

Find revision guides, exam papers and sample essays amongst hundreds of free resources available to students.

Find resources any subjects

Maths resources | Science resources | Music resources | Spanish resources | English resources | French resources