# Ib Maths Tutors-Types of functions(part-3)

IB Maths Tutors should give a fair number of hours in teaching functions.This is my third article on functions in the series of ib mathematics

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here.

**1.Greatest Integer Function**– This is an interesting function. It is defined as the largest integer less than or equal to x

* y*

**= [**

*x*].For all real numbers, *x*, this function gives the largest integer less

than or equal to *x*.

For example: ** [1] = 1 [2.5] = 2 [4.7] = 4 [5.3] = 5**

*Beware!*** [-2] = -2 [-2.6] = -3 [-4.1] = -5 [-6.5] = -7**

domain=**R**

range=**Z**

**2. Fractional part function-**

for every real value of x this function gives the fractional part of x.

** f(x)={x}**

** {2.3}=.3 , {5.4}=.4, {2.2}=.2**

** {6.7}=.7, {-2.3}=.7, {-2.6}=.3**

We can say that: ** 0≤{x}∠1**

domain=**R**

range=**less than 1**

**3. Polynomial function**– These are functions of the form

** f(x) = a _{n}x^{n} + a_{n−1}x ^{n−1} + . . . + a_{2}x ^{2 }+ a_{1}x + a_{0 }.**

Constant, linear, quadratic, cubic, quartic functions etc fall in this category

domain of these functions is R and range is either** R** or a subset of **R
**

** **

**4. Trigonometric functions- **Trigonometric functions or circular functions draw the relationship between the sides and angles of right triangles .we can find this relationship using **“unit circle”**. I have explained all this thing in the given video.

https://www.youtube.com/edit?video_id=r5C2oSawETs&video_referrer=watch

There are six trigonometric functions, we will discuss them all one by one

**i. Sin function(variation in a)**–

** f(x)=sin x**

this is a periodic function with a period of** 2Π**

domain=**R**

range=**[-1,1]**

**ii. Cosine function(variation in b)-**

**f(x)=cosx**

this is also a periodic function with a period of **2Π**

domain=**R**

range=**[-1,1]**

**iii. Tangent function(variation in a/b)- **

** f(x)= tan x**

this is also a periodic function with a period of pie

domain=**R-{npie+pie/2}**

range=**R**

this was my last post in ib maths tutors-function series. In my next post i will give yoy some questions based on these topics