{"id":4052,"date":"2021-08-15T14:49:02","date_gmt":"2021-08-15T14:49:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4052"},"modified":"2022-01-16T16:56:54","modified_gmt":"2022-01-16T11:26:54","slug":"types-of-functions-in-maths","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/","title":{"rendered":"Types of Functions in Maths – Domain and Range"},"content":{"rendered":"

Here you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.<\/p>\n

Let’s begin –<\/p>\n

Types of Functions in Maths<\/h2>\n

(a) Polynomial function<\/strong><\/h4>\n

If a function is defined by f(x) = \\(a_0x^n\\) + \\(a_1x^{n-1}\\) + \\(a_2x^{n-2}\\) + ….. + \\(a_{n-1}x\\) + \\(a_n\\) where n is a non negative integer and \\(a_0\\), \\(a_1\\), \\(a_2\\), ….. , \\(a_n\\) are real numbers and \\(a_0\\) \\(\\ne\\) 0, then f is called a polynomial function of degree n. If n is odd, then polynomial is of odd degree, if n is even, then the polynomial is of even degree.<\/p>\n

Note :<\/strong><\/p>\n

(i)  Range of odd degree polynomial is always R.<\/p>\n

(ii)  Range of even degree polynomial is never R.<\/p>\n

(iii)  A Polynomial of degree one with no constant term is called an odd linear function. i.e. f(x) = ax,
a \\(\\ne\\) 0<\/p>\n

(iv)  f(x) = ax + b, a \\(\\ne\\) 0 is a linear polynomial.<\/p>\n

(v)  f(x) = c, is a non linear polynomial(its degree is zero).<\/p>\n

(vi)  f(x) = 0, is a polynomial but its degree is not defined.<\/p>\n

(vii)  There are two polynomial functions, satisfying the relation;<\/p>\n

f(x).f(1\/x) = f(x) + f(1\/x). They are :<\/p>\n

(a)  f(x) = \\(x^n\\) + 1   and   (b)  f(x) = 1 – \\(x^n\\), where n is a positive integer.<\/p>\n

(b) Algebraic Function<\/strong><\/h4>\n

A function f is called an algebraic function if it can be constructed using algebraic operations(such as addition, subtraction, multiplication, division, and taking radicals) within polynomials.<\/p>\n

Note :<\/strong><\/p>\n

(i)  All polynomial functions are algebraic but not the converse.<\/p>\n

(ii)  A function that is not algebraic is called Transcendental function.<\/p>\n

(c) Rational Function<\/strong><\/h4>\n

A rational function is a function of the form y = f(x) = \\(g(x)\\over h(x)\\), where g(x) & h(x) are polynomials & h(x) \\(\\ne\\) 0,<\/p>\n

Domain :<\/strong>  R – {x | h(x) = 0}<\/p>\n

Any algebraic function is automatically an algebraic function.<\/p>\n

(d) Trigonometric Functions<\/strong><\/h4>\n\n\n

(i) Sine Function<\/h4>\n\n\t\t

f(x) = sinx
\n\t\t Domain :<\/b> R
\n\t\t Range :<\/b> [-1, 1], period 2\\(\\pi\\)<\/p>
\n\n\t\t

(ii) Cosine Function<\/h4>\n\n\t\t

f(x) = cosx
\n\t\t Domain :<\/b> R
\n\t\t Range :<\/b> [-1, 1], period 2\\(\\pi\\)<\/p>
\n\n\t\t

(iii) Tangent Function<\/h4>\n\n\t\t

f(x) = tanx
\n\t\t Domain :<\/b> R – {x | x = \\({(2n+1)\\pi\\over 2}\\), n \\(\\in\\) I }
\n\t\t Range :<\/b> R, period \\(\\pi\\)<\/p>
\n\n\t\t

(iv) Cosecant Function<\/h4>\n\n\t\t

f(x) = cosecx
\n\t\t Domain :<\/b> R – { x | x = n\\(\\pi\\), n \\(\\in\\) I }
\n\t\t Range :<\/b> R – (-1, 1), period 2\\(\\pi\\)<\/p>
\n\n\t\t

(v) Secant Function<\/h4>\n\n\t\t

f(x) = secx
\n\t\t Domain :<\/b> R – { x | x = (2n+1)\\(\\pi\\)\/2, n \\(\\in\\) I }
\n\t\t Range :<\/b> R – (-1, 1), period 2\\(\\pi\\)<\/p>
\n\n\t\t

(vi) Cotangent Function<\/h4>\n\n\t\t

f(x) = cotx
\n\t\t Domain :<\/b> R – { x | x = n\\(\\pi\\), n \\(\\in\\) I }
\n\t\t Range :<\/b> R, period \\(\\pi\\)

<\/p>\n\n\n

(e) Exponential and Logarithmic function<\/strong><\/h4>\n

A function f(x) = \\(a^x\\)(a > 0), a \\(\\ne\\) 1, x \\(\\in\\) R is called an exponential function. The inverse of the exponential function is called the logarithmic function, i.e. g(x) = \\(log_ax\\).<\/p>\n

Note that f(x) & g(x) are inverse of each other.<\/p>\n

Domain  of \\(a^x\\) is R  Range \\(R^+\\)<\/p>\n

Domain of \\(log_ax\\) is \\(R^+\\)  Range  R<\/p>\n

(f) Absolute Value Function<\/strong><\/h4>\n

A function y = f(x) = |x| is called the absolute value function or modulus function. It is defined as :<\/p>\n

y = |x| = [x if x \\(\\le\\) 0   -x if x < 0]<\/p>\n

For f(x) = |x|, domain is R and range is [0,\\(\\infty\\)]<\/p>\n

For f(x) = \\(1\\over{|x|}\\), domain is R – {0} and range is \\(R^+\\)<\/p>\n

(g) Signum Function<\/strong><\/h4>\n

A function y = f(x) = Sgn(x) is defined as follows :<\/p>\n

y = f(x) = [ 1 for x > 0    0 for x = 0  -1 for x < 0 ]<\/p>\n

Domain : R<\/p>\n

Range : [-1, 0, 1]<\/p>\n

(h) Greatest integer or step up function<\/strong><\/h4>\n

The function y = f(x) = [x] is called the greatest integer function where [x] denotes the greatest integer less than or equal to x. Note that for :<\/p>\n\n\n\n \n \n \n \n \n
x<\/td>\n [x]<\/td>\n <\/tr>\n
[-2,-1]<\/td>\n -2<\/td>\n <\/tr>\n
[-1,0]<\/td>\n -1<\/td>\n <\/tr>\n
[0,1]<\/td>\n 0<\/td>\n <\/tr>\n
[1,2]<\/td>\n 1<\/td>\n <\/tr>\n <\/tbody><\/table>
\n Domain :<\/b> R
\n Range :<\/b> I\n

<\/p>\n\n\n

(i) Fractional part function<\/strong><\/h4>\n

It is defined as : g(x) = {x} = x – [x] e.g. the fractional part of the number 2.1 is 2.1 – 2 = 0.1 and the fractional part of -3.7 is 0.3. The period of this function is 1.<\/p>\n

(j) Identity function<\/strong><\/h4>\n

The function f : A \\(\\rightarrow\\) A defined by f(x) = x \\(\\forall\\) x \\(\\in\\) A is called the identity of A and is denoted by \\(I_A\\). It is easy to observe that identity function defined on R is bijection.<\/p>\n

(j) Constant function<\/strong><\/h4>\n

The function f : A \\(\\rightarrow\\) B is said to be a constant function if every element of A has the same f image in B. Thus f : A \\(\\rightarrow\\) B ; f(x) = c, \\(\\forall\\) x \\(\\in\\) A, c \\(\\in\\) B is a constant function. Note that the range of constant function is singleton.<\/p>\n

Hope you learnt types of functions in maths and to learn more practice more questions and get ahead in competition. Good Luck!<\/p>\n\n\n

\n
Next – Domain and Range of Greatest Integer Function<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – How to Find Domain and Range of Function<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range. Let’s begin – Types of Functions in Maths (a) Polynomial function If a function is defined by f(x) = \\(a_0x^n\\) + \\(a_1x^{n-1}\\) + \\(a_2x^{n-2}\\) + ….. + \\(a_{n-1}x\\) + \\(a_n\\) where n is a non …<\/p>\n

Types of Functions in Maths – Domain and Range<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[359,358],"yoast_head":"\nTypes of Functions in Maths - Domain and Range - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Types of Functions in Maths - Domain and Range - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-15T14:49:02+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-01-16T11:26:54+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Types of Functions in Maths – Domain and Range\",\"datePublished\":\"2021-08-15T14:49:02+00:00\",\"dateModified\":\"2022-01-16T11:26:54+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\"},\"wordCount\":840,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"function\",\"types of functions in maths\"],\"articleSection\":[\"Function\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\",\"url\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\",\"name\":\"Types of Functions in Maths - Domain and Range - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-08-15T14:49:02+00:00\",\"dateModified\":\"2022-01-16T11:26:54+00:00\",\"description\":\"In this post you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Types of Functions in Maths – Domain and Range\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Types of Functions in Maths - Domain and Range - Mathemerize","description":"In this post you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/","og_locale":"en_US","og_type":"article","og_title":"Types of Functions in Maths - Domain and Range - Mathemerize","og_description":"In this post you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.","og_url":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/","og_site_name":"Mathemerize","article_published_time":"2021-08-15T14:49:02+00:00","article_modified_time":"2022-01-16T11:26:54+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Types of Functions in Maths – Domain and Range","datePublished":"2021-08-15T14:49:02+00:00","dateModified":"2022-01-16T11:26:54+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/"},"wordCount":840,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["function","types of functions in maths"],"articleSection":["Function"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/types-of-functions-in-maths\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/","url":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/","name":"Types of Functions in Maths - Domain and Range - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-08-15T14:49:02+00:00","dateModified":"2022-01-16T11:26:54+00:00","description":"In this post you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/types-of-functions-in-maths\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/types-of-functions-in-maths\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Types of Functions in Maths – Domain and Range"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/4052"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=4052"}],"version-history":[{"count":7,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/4052\/revisions"}],"predecessor-version":[{"id":9547,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/4052\/revisions\/9547"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=4052"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=4052"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=4052"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}