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}                                       

                                   
Range    = {k}

2.Identity Function-

                                                  F(x)=x
Domain=  ℝ
Range   =   ℝ

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

 

3.Linear Function-

                                                    F(x)=mx+c
Domain=  ℝ

Range   =   ℝ

linear function.. 

4.Quadratic Function-

                                                       F(x)=x2
Domain=  ℝ

Range    =(0, ∞]

quadratic-function 

5.Cube Function-

                                                     F(x)=x3
Domain=   ℝ

Range    =   ℝ

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=   ℝ

Range    ={0,1}

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 of its negative sign, if it is negative.
Domain=  ℝ
Range   = [0, ∞)

 

 

 

 

9.Exponential Function-

F(x)=  ex
Domain=  ℝ

Range    =(0,∞)

exponential-function 

10.Logarithmic Function-

                                                 F(x)=lnx
Range     =  ℝ

Domain   = (0,∞)

logarithim-function 

11.Exponential Function-

                                              F(x)=  ex
Domain=  ℝ

Range    =(0,∞)

exponential-function 

Notice what happen if we draw F(x)=ex 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!!)

inverse of each otherAlso 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

ib free demo class