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

<img src="ibmathstutors.jpg" alt="ibmathstutors">

greatest integer function

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

<img src="ibmathstutors.jpg" alt="ibmathstutors">

Fractional Part

3. Polynomial function–    These are functions of the form

       f(x) = anxn + an−1x n−1 + . . . + a2x 2 + a1x + a0 .

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

<img src="ibmathstutors.jpg2" alt="ibmathstutors2">

polynomial

 

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

domain=R
range=[-1,1]

<img src="ibmathstutors.jpg3" alt="ibmathstutors3">

Sin function

ii. Cosine function(variation in b)-

f(x)=cosx

this is also a periodic function with a period of

domain=R

range=[-1,1]

<img src="ibmathstutors.jpg4" alt="ibmathstutors4">

cosine function

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

<img src="ibmathstutors.jpg5" alt="ibmathstutors">

tan function

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

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