{"id":33476,"date":"2023-08-25T21:16:00","date_gmt":"2023-08-25T21:16:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33476"},"modified":"2023-08-27T09:32:39","modified_gmt":"2023-08-27T09:32:39","slug":"identity-function-definition-graph-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function","title":{"rendered":"Identity Function: Definition, Graph, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-2b2da1d8-2fad-4ff7-a065-bc6b87592dc9\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function#0-what-is-identity-function>What Is Identity Function?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function#2-domain-and-range-of-identity-function>Domain and Range of Identity Function<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function#5-properties-of-identity-function>Properties of Identity Function<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function#6-solved-examples-on-identity-function>Solved Examples on Identity Function<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function#7-practice-problems-on-identity-function>Practice Problems on Identity Function<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function#8-frequently-asked-questions-about-identity-function>Frequently Asked Questions about Identity Function<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-identity-function\">What Is Identity Function?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>An identity function is a polynomial function that maps every element to itself. So, the image of any element is the element itself. It is a function in which the output is the same as the input.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Identity function is denoted by &#8220;I&#8221; and it has the form I(x) = x for all real numbers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An identity function is also known as an <strong>identity map,<\/strong> <strong>identity relation<\/strong> or <strong>identity transformation<\/strong>. It is known as an identity function because the image of an element in the domain is the same as the output in the range. The identity of the element is maintained.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identity-quarter-hours\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_qrtr_hrs_tell_time_words_pt.png\" alt=\"Identity Quarter Hours Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identity Quarter Hours Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-identity-function-definition\">Identity Function Definition<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Identity function is a real-valued function <\/strong>$f\\:R \\rightarrow R$<strong> such that <\/strong>$f(x) = x$<strong> for all <\/strong>$x\\;\\in \\;R$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An identity function maps each real number to itself. The preimage and the image are equal for identity functions.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"459\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/mapping-diagram-of-identity-function.png\" alt=\"Mapping diagram of identity function\" class=\"wp-image-33482\" title=\"Mapping diagram of identity function\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/mapping-diagram-of-identity-function.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/mapping-diagram-of-identity-function-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">It is noted from the above image that the function f is an identity function as each element of A is mapped onto itself. Hence, the function f is one-one and onto.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-domain-and-range-of-identity-function\">Domain and Range of Identity Function<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The domain of the identity function is R, the set of real numbers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The range of the identity function is also R.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The co-domain and the range of an identity function are equal sets.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the identity function is onto.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-inverse-of-identity-function\">Inverse of Identity Function<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When we find the inverse of any function, the domain and range of that function gets exchanged. This implies that the identity function is invertible and is its own inverse.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Identity function takes an element and maps it to itself.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Inverse of the identity function (which is itself) again maps the same element to itself.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-identity-function-graph\">Identity Function Graph<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To graph the identity function, we plot the different points as shown below.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>x<\/td><td>-4<\/td><td>-3<\/td><td>-2<\/td><td>-1<\/td><td>0<\/td><td>1<\/td><td>2<\/td><td>3<\/td><\/tr><tr><td>I(x)<\/td><td>-4<\/td><td>-4<\/td><td>-2<\/td><td>-1<\/td><td>0<\/td><td>1<\/td><td>2<\/td><td>3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The graph of the identity function is a straight line that passes through the origin.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The straight line makes an angle of 45\u00b0 with the positive x-axis.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Slope of a straight line = tan \u03b8 where \u03b8 is the angle between line and positive x-axis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, slope of an identity function graph = tan 45\u00b0 = 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"665\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/identity-function-graph.png\" alt=\"Identity function graph\" class=\"wp-image-33483\" title=\"Identity function graph\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/identity-function-graph.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/identity-function-graph-280x300.png 280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-properties-of-identity-function\">Properties of Identity Function<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It is a real-valued linear function.<\/li>\n\n\n\n<li>The graph of an identity function is a straight line that makes an angle of 45\u00b0 with both x-axis and y-axis.<\/li>\n\n\n\n<li>Identity function is bijective.&nbsp;<\/li>\n\n\n\n<li>The inverse of the identity function is the identity function itself.<\/li>\n\n\n\n<li>Identity function is an odd function since $I(x) \/neq I(\\;-\\;x)$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-identity-function\">Solved Examples on Identity Function<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. <\/strong><strong>If g is an identity function, then find g(0), g(1), g(100), g(6.4).<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g is an identity function. So, it will return the same value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g(0) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g(1) = 1&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g(100) = 100&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g(6.4) = 6.4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. What is the domain of the identity function?&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Domain of the identity function is the set of real numbers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Identity function maps every real number to itself.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Define an identity function. What is the graph of identity function?&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An identity function is defined as a real-valued function f : R \u2192 R such that f(x) = x for all x in R.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Its graph is a straight line passing through the origin.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"510\" height=\"511\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-identity-function.png\" alt=\"Graph of identity function\" class=\"wp-image-33485\" title=\"Graph of identity function\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-identity-function.png 510w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-identity-function-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-identity-function-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-identity-function-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-identity-function-120x120.png 120w\" sizes=\"auto, (max-width: 510px) 100vw, 510px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-identity-function\">Practice Problems on Identity Function<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Identity Function: Definition, Graph, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The identity function will map the real number 0 to<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">0<\/div><div class=\"spq_answer_block\" data-value=\"2\">10<\/div><div class=\"spq_answer_block\" data-value=\"3\">x<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 0<br\/>The identity function returns the same value.<br>\r\nThus, I(0) = 0<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is the domain of an identity function?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Complex Numbers<\/div><div class=\"spq_answer_block\" data-value=\"1\">Integers<\/div><div class=\"spq_answer_block\" data-value=\"2\">Real Numbers<\/div><div class=\"spq_answer_block\" data-value=\"3\">Natural Numbers<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Real Numbers<br\/>The identity function is defined as f: R \u2192 R such that f(x) = x.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The identity function has the form<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">f(x) = 1<\/div><div class=\"spq_answer_block\" data-value=\"1\">f(x) = $x^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">f(x) = c<\/div><div class=\"spq_answer_block\" data-value=\"3\">f(x) = x<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: f(x) = x<br\/>The identity function is defined as f: R \u2192 R such that f(x) = x.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following is a slope of the graph of an identity function?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">not defined<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The identity function is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">only onto<\/div><div class=\"spq_answer_block\" data-value=\"1\">only one-one<\/div><div class=\"spq_answer_block\" data-value=\"2\">one-one and onto<\/div><div class=\"spq_answer_block\" data-value=\"3\">many to one<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: one-one and onto<br\/>The identity function is bijective. 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         }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"f(x) = $$x^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity function is defined as f: R \u2192 R such that f(x) = x.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"f(x) = c\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity 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            \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is a slope of the graph of an identity function?\",\n                    \"text\": \"Which of the following is a slope of the graph of an identity function?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"not defined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"\u03b8 = 45\u00b0<br>\r\nSlope (m) = tan 45\u00b0 = 1\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The identity function is\",\n                    \"text\": \"The identity function is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The identity function is bijective. Thus, it is one-one and onto.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"only onto\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity function is bijective. Thus, it is one-one and onto. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"only one-one\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity function is bijective. Thus, it is one-one and onto. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"many to one\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity function is bijective. Thus, it is one-one and onto. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"one-one and onto\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The identity function is bijective. Thus, it is one-one and onto. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The identity function is bijective. Thus, it is one-one and onto. \"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-about-identity-function\">Frequently Asked Questions about Identity Function<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-949f4a87-a8bb-4442-99ec-346f0343dd13\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-949f4a87-a8bb-4442-99ec-346f0343dd13\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-949f4a87-a8bb-4442-99ec-346f0343dd13\"><strong>What is the difference between a constant function and an identity function?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-949f4a87-a8bb-4442-99ec-346f0343dd13\">\n\n<p class=\"wp-block-paragraph\">A constant function is a function whose output remains the same irrespective of the input. It is defined as f(x) = c, where x \u2208 R. On the other hand, an identity function is a function that returns the same value. It is defined as\u00a0 f(x) = x, where x \u2208 R.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-949f4a87-a8bb-4442-99ec-346f0343dd13\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-949f4a87-a8bb-4442-99ec-346f0343dd13\"><strong>What is a many-to-one function?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-949f4a87-a8bb-4442-99ec-346f0343dd13\">\n\n<p class=\"wp-block-paragraph\">According to the many-to-one function, the two or more different elements are mapped to the same image. One example of this function is:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"233\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/many-to-one-function.png\" alt=\"Understanding Many to One functions\" class=\"wp-image-33480\" title=\"Understanding Many to One functions\"\/><\/figure>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-949f4a87-a8bb-4442-99ec-346f0343dd13\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-949f4a87-a8bb-4442-99ec-346f0343dd13\"><strong>Is identity function even or odd?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-949f4a87-a8bb-4442-99ec-346f0343dd13\">\n\n<p class=\"wp-block-paragraph\">Identity function is an odd function.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f(x) = x is an identity function.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f( \u2013 x) =  \u2013 x<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Identity Function? An identity function is a polynomial function that maps every element to itself. So, the image of any element is the element itself. It is a function in which the output is the same as the input.&nbsp; Identity function is denoted by &#8220;I&#8221; and it has the form I(x) = x &#8230; <a title=\"Identity Function: Definition, Graph, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/identity-function\" aria-label=\"More on Identity Function: Definition, Graph, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-33476","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33476","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=33476"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33476\/revisions"}],"predecessor-version":[{"id":33492,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33476\/revisions\/33492"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33476"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33476"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}