{"id":234,"date":"2017-05-22T01:39:45","date_gmt":"2017-05-21T20:09:45","guid":{"rendered":"http:\/\/ibelitetutor.com\/blog\/?p=234"},"modified":"2024-05-22T15:00:57","modified_gmt":"2024-05-22T09:30:57","slug":"ib-mathematics-tutors-types-of-functions","status":"publish","type":"post","link":"https:\/\/ibelitetutor.com\/blog\/ib-mathematics-tutors-types-of-functions\/","title":{"rendered":"IB Mathematics Tutors- types of mathematical function(part-1)"},"content":{"rendered":"

IB Mathematics Tutors<\/strong> should give a fair number of hours in teaching functions. This is my third article on functions in the series of ib mathematics<\/p>\n

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here<\/p>\n

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here
\n1.Constant Function-<\/strong>
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 F(x)=k<\/strong>
\nDomain= \u211d \u00a0 \u00a0<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Range\u00a0\u00a0\u00a0 = {k}\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong>
\nRange\u00a0\u00a0\u00a0 = {k}<\/strong><\/p>\n

<\/p>\n

2.Identity Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 F(x)=x<\/strong>
\nDomain=\u00a0 \u211d<\/strong>
\nRange\u00a0\u00a0 = \u00a0 \u211d<\/strong><\/p>\n

\"<img
identity-function<\/figcaption><\/figure>\n

 <\/p>\n

3.Linear Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 F(x)=mx+c<\/strong>
\nDomain=\u00a0 \u211d<\/strong><\/p>\n

Range \u00a0 = \u00a0 \u211d<\/strong><\/p>\n

\nlinear function.. <\/p>\n

4.Quadratic Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0F(x)=x2<\/sup><\/strong>
\nDomain= \u00a0\u211d<\/strong><\/p>\n

Range\u00a0\u00a0\u00a0 =(0, \u221e]<\/strong><\/p>\n

\nquadratic-function <\/p>\n

5.Cube Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0F(x)=x3<\/sup><\/strong>
\nDomain= \u00a0 \u211d<\/strong><\/p>\n

Range\u00a0\u00a0\u00a0 = \u00a0 \u211d<\/strong><\/p>\n

\ncubic-function <\/p>\n

6.Reciprocal Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0F(x)=1\/x<\/strong>
\nDomain= \u00a0 \u211d-{0}<\/strong><\/p>\n

Range\u00a0\u00a0\u00a0 = \u211d-{0}<\/strong><\/p>\n

 <\/p>\n

7.Step Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 F(x)=0 \u00a0 \u00a0if \u00a0 x\u22200<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 =1 \u00a0 if \u00a0 x\u22650<\/strong>
\nDomain= \u00a0 \u211d<\/strong><\/p>\n

Range\u00a0\u00a0\u00a0\u00a0={0,1}<\/strong><\/p>\n

\nstep-function <\/p>\n

8. Absolute value Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0F(x)=|x|<\/strong>\u00a0\u00a0\u00a0\u00a0 = x\u00a0\u00a0\u00a0 if x\u22650<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 =-x\u00a0 if x\u22200<\/strong>
\nBasically, this function gives the magnitude of a number and strips it of its negative sign, if it is negative.
\nDomain=\u00a0 \u211d<\/strong>
\nRange\u00a0\u00a0 = [0, \u221e)<\/strong><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

9.Exponential Function-<\/strong><\/p>\n

F(x)= \u00a0ex<\/sup><\/strong>
\nDomain=\u00a0 \u211d<\/p>\n

Range\u00a0\u00a0\u00a0\u00a0=(0,\u221e)<\/strong><\/p>\n

\nexponential-function <\/p>\n

10.Logarithmic Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0F(x)=lnx<\/strong>
\nRange\u00a0\u00a0\u00a0\u00a0 =\u00a0 \u211d<\/strong><\/p>\n

Domain\u00a0\u00a0\u00a0= (0,\u221e)<\/strong><\/p>\n

\nlogarithim-function <\/p>\n

11.Exponential Function-<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong>\u00a0F(x)= \u00a0ex<\/sup><\/strong>
\nDomain=\u00a0 \u211d<\/strong><\/p>\n

Range\u00a0\u00a0\u00a0\u00a0=(0,\u221e)<\/strong><\/p>\n

\nexponential-function <\/p>\n

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

\ninverse of each otherAlso note what happens if we operate F(x)=lnx<\/strong> function and then g(x)=ex<\/sup><\/strong> function on a particular x, in any order.
\nthat is F(g(x))=x<\/strong> and g(f(x))=x<\/strong>
\nthese types of functions are called inverse functions
\nIn my next article on IB Mathematics Tutors series, I will write more about types of functions<\/p>\n

\"ib<\/p>\n\n

\n

<\/p>

    <\/ul><\/div>\n
    \n
    \n<\/fieldset>\n

    \n<\/p>

    <\/div>\n<\/form>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"

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