[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143367-105":59,"doc-detail-143367-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","function-basics-function-basics-mathpro-by-lazizbek","Function basics - Function basics - MathPro by Lazizbek","","A concise math primer introduces the core idea of a function as a machine mapping one input value to exactly one output. It explains domain as the complete set of valid inputs and range as the complete set of outputs the function can produce. The material then reviews common number types—natural, whole, integers, rational, irrational, and real—highlighting their defining properties and typical examples, supporting clear understanding before further practice.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/function-basics-function-basics-mathpro-by-lazizbek/143367/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/function-basics-function-basics-mathpro-by-lazizbek/143367.png","ImageObject",300,407,{"name":92,"@type":93},"Ivy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-02","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is a function in mathematics?","Question",{"text":112,"@type":113},"A function takes an input value and produces exactly one output. It is written as f(x), where x is the input and f(x) is the output.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are domain and range defined for a function?",{"text":117,"@type":113},"The domain is the set of all possible inputs x that can be used without breaking math rules. The range is the set of all outputs values that f(x) can produce.",{"name":119,"@type":110,"acceptedAnswer":120},"What distinguishes rational numbers from irrational numbers?",{"text":121,"@type":113},"Rational numbers can be written as a fraction of two integers with a nonzero denominator, and their decimals either terminate or repeat. Irrational numbers cannot be expressed as such fractions and have non-terminating, non-repeating decimal expansions.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},143367,1790293765,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},549758252649,"https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819","􀂶  \nFunction basics | MathPro by Lazizbek  \n# Function?\n\nA function is like a machine where you put in one value (the input), and it gives  \nyou exactly one output in return. Mathematically, if we have a function  f(x) , it  \ntakes an input  x  and produces an output  f(x) .  \n## Domain — input?\n\nThe domain is the set of all possible input values for a function. In other words, it ʼsall the values of  x  that we can use in the function without breaking any math  \nrules.  \n## Range — output?\n\nThe range is the set of all possible output values, or all the values that  f(x)  can  \nproduce.  \n# Numbers?\n\n Natural Numbers􀗤 These are the counting numbers starting from 1, 2, 3, andso on. They are used for counting objects and are always positive. Example:  \n1,2,3, …  \n Whole Numbers􀗤 Whole numbers include all natural numbers and zero. Thisset does not include negative numbers or fractions. Example: 0,1,2,3, …  \n Integers􀗤 Integers include all whole numbers and their negative counterparts.They can be positive, negative, or zero, but do not include fractions or  \ndecimals. Example: …, 􀘂3, 􀘂2,􀘂1,0,1,2,3, …  \n Rational Numbers􀗤 Rational numbers are any numbers that can be written as afraction of two integers, where the denominator is not zero. They can be  \nFunction basics | MathPro by Lazizbek 1  \nterminating or repeating decimals.  \n Irrational Numbers􀗤 These are numbers that cannot be expressed as afraction of two integers. Their decimal expansions are non-terminating andnon-repeating. Example: π, √ 2, π/2 .  \n Real Numbers􀗤 The set of real numbers includes all rational and irrationalnumbers. They represent any value along the continuous number line,covering all possible decimal expansions.  \nFunction basics | MathPro by Lazizbek 2  \n# Practice part\n\nFunction basics | MathPro by Lazizbek 3  \nFunction basics | MathPro by Lazizbek 4  \nInverse functions?  \nFunction basics | MathPro by Lazizbek 5  \nFunction basics | MathPro by Lazizbek 6  \ndesmos.com  \n# Composite function\n\nFunction basics | MathPro by Lazizbek 7","cbCaiiPoyCGXmLan","https://ap.wps.com/l/cbCaiiPoyCGXmLan","pdf",339422,"English","# Function?\n## Domain — input?\n## Range — output?\n# Numbers?\n## Natural Numbers\n## Whole Numbers\n## Integers\n## Rational Numbers\n## Irrational Numbers\n## Real Numbers\n# Practice part\n# Composite function\n# Inverse functions?","[{\"question\":\"What is a function in mathematics?\",\"answer\":\"A function takes an input value and produces exactly one output. It is written as f(x), where x is the input and f(x) is the output.\"},{\"question\":\"How are domain and range defined for a function?\",\"answer\":\"The domain is the set of all possible inputs x that can be used without breaking math rules. The range is the set of all outputs values that f(x) can produce.\"},{\"question\":\"What distinguishes rational numbers from irrational numbers?\",\"answer\":\"Rational numbers can be written as a fraction of two integers with a nonzero denominator, and their decimals either terminate or repeat. Irrational numbers cannot be expressed as such fractions and have non-terminating, non-repeating decimal expansions.\"}]","Function basics - Function basics - MathPro by Lazizbek | PDF",1787694716,18]