## An Introduction to Functions in Mathematics

In** IB Maths Tuition** both HL and SL, 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.

Suppose I say that:

** y=x² **

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

** y=f(x)**

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

** x=f(y) **

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

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.) Suppose you are driving a car, then your location is a function of time. As time changes, your location changes.

2.) 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

** V=f(R)**

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

** P=f(I)**

4) 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

** G=f(H.W)**

**Functions as Relations- Functions can also be understood as a special type of relations. that means all ordered pairs are relations but all relations are not functions. Functions are a subset of relations**

if we have a function like:

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.

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

FUNCTIONS_graphs.pdf

**Domain and Range of functions**