IB Mathematics Tutors- types of mathematical function(part-1)

IB Mathematics 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.Constant Function-
                                                F(x)=k
Domain= ℝ    

                                            Range    = {k}                                       

<img src="constant-function.jpg" alt="constant-function">

constant-function

                                   
Range    = {k}

2.Identity Function-

                                                  F(x)=x
Domain= 
Range   =  

<img src="identity-function.jpg" alt="identity-function">

identity-function

 

3.Linear Function-

                                                    F(x)=mx+c
Domain=  ℝ

Range   =  

<img src="linear-function.jpg" alt="linear-function">

linear function..

 

4.Quadratic Function-

                                                       F(x)=x2
Domain=  ℝ

Range    =(0, ∞]

<img src="quadratic-function.jpg" alt="quadratic-function">

quadratic-function

 

5.Cube Function-

                                                     F(x)=x3
Domain=  

Range    =  

<img src="cubic-function.jpg" alt="cubic-function">

cubic-function

 

6.Reciprocal Function-

                                                   F(x)=1/x
Domain=   ℝ-{0}

Range    = ℝ-{0}

 

7.Step Function-

                                                    F(x)=0    if   x∠0

                                                            =1   if   x≥0
Domain=  

Range    ={0,1}

<img src="step-function.jpg" alt="step-function">

step-function

 

8.Absolute value Function-

                                                 F(x)=|x|     = x    if x≥0

                                                        =-x  if x∠0
Basically, this function gives the magnitude of a number and strips it off its negative sign, if it is negative.
Domain= 
Range   = [0, ∞)

<img src="modulus-function.jpg" alt="modulus-function">

 

 

 

9.Exponential Function-

F(x)=  ex
Domain=  ℝ

Range    =(0,∞)

<img src="exponential-function.jpg" alt="exponential-function">

exponential-function

 

10.Logarithmic Function-

                                                 F(x)=lnx
Range     = 

Domain   = (0,∞)

<img src="lograthemic-function.jpg" alt="lograthemic-function">

logarithim-function

 

11.Exponential Function-

                                              F(x)=  ex
Domain= 

Range    =(0,∞)

<img src="exponential-function.jpg" alt="ib tutors">

exponential-function

 

Notice what happen if we draw F(x)=e   and F(x)=lnx on the same axis
the graph of each function seems to be mirror reflections of each other in the line y=x
(In fact, they are!!)

<img src="lograthemic-function.jpg" alt="ib tutions">

inverse of each other

Also note what happens if we operate F(x)=lnx function and then g(x)=ex function on a particular x, in any order.
that is F(g(x))=x and g(f(x))=x
these types of functions are called inverse functions
In my next article on IB Mathematics Tutors series, I will write more about types of functions

 

 

 

 

 

 

 

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