{"id":272,"date":"2017-05-28T00:42:37","date_gmt":"2017-05-27T19:12:37","guid":{"rendered":"http:\/\/ibelitetutor.com\/blog\/?p=272"},"modified":"2024-05-22T14:55:19","modified_gmt":"2024-05-22T09:25:19","slug":"types-of-function","status":"publish","type":"post","link":"https:\/\/ibelitetutor.com\/blog\/types-of-function\/","title":{"rendered":"Types of functions(part-3)"},"content":{"rendered":"

Types of Functions-<\/h2>\n

IB Maths Tutors<\/a> <\/span>should give twenty-two hours for teaching functions and equations as per IBO recommendations. This is my third article on functions in the series of ib mathematics<\/p>\n

IB Maths Tutors should give twenty hours in teaching functions and equations. This is my third article on functions in the series of ib mathematics<\/p>\n

As you know there are many different\u00a0types of functions in Mathematics. Here I am discussing a few very important of them<\/p>\n

 <\/p>\n

1.Greatest Integer Function<\/strong>– \u00a0This is an interesting function. It is defined as the largest \u00a0 \u00a0 integer less than or equal to x<\/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 \u00a0y<\/strong><\/em>\u00a0= [x<\/em>].<\/strong><\/p>\n

For all real numbers,\u00a0x<\/em>, this function gives the largest integer less
\nthan or equal to\u00a0x<\/em>.<\/p>\n

For example:\u00a0\u00a0 [1] = 1\u00a0\u00a0\u00a0\u00a0\u00a0 [2.5] = 2\u00a0\u00a0\u00a0\u00a0\u00a0 [4.7] = 4\u00a0\u00a0\u00a0\u00a0\u00a0 [5.3] = 5<\/strong>
\nBeware!<\/em><\/strong>\u00a0\u00a0\u00a0 [-2] = -2\u00a0\u00a0\u00a0\u00a0\u00a0 [-2.6] = -3\u00a0\u00a0\u00a0\u00a0\u00a0 [-4.1] = -5\u00a0\u00a0\u00a0\u00a0\u00a0 [-6.5] = -7<\/strong><\/p>\n

domain=R<\/strong>
\nrange=Z<\/b><\/p>\n

\n

greatest integer function2. Fractional part function-<\/strong><\/p>\n

for every real value of x this function gives the fractional part of x.<\/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 f(x)={x}<\/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 {2.3}=.3 , {5.4}=.4, {2.2}=.2<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 {6.7}=.7, {-2.3}=.7, {-2.6}=.3<\/strong><\/p>\n

We can say that: \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 0\u2264{x}\u22201<\/strong><\/p>\n

domain=R<\/strong>
\nrange=less than 1<\/b><\/p>\n

3. Polynomial function<\/strong>– \u00a0 \u00a0These are functions of the form<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0f(x) = an<\/sub>xn<\/sup> + an\u22121<\/sub>x n\u22121<\/sup> + . . . + a2<\/sub>x 2 <\/sup>+ a1<\/sub>x + a0 <\/sub>.<\/strong><\/p>\n

Constant, linear, quadratic, cubic, quartic functions etc fall in this category
\ndomain of these functions is R and range is either R<\/strong> or a subset of R
\n<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

4. Trigonometric functions- \u00a0<\/strong>Trigonometric functions or circular functions draw the relationship between the sides and angles of right triangles .we can find this relationship using \u201cunit circle\u201d<\/strong>. I have explained all this thing in the given video.<\/p>\n