[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-316232-105":59,"doc-detail-316232-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","mathematical-methods-glossary-unit-1-functions-and-graphs","Mathematical Methods Glossary - Unit 1 - Functions and graphs","","A glossary-style reference organized by curriculum units for senior secondary Mathematical Methods. Definitions and key properties cover core topics in functions and graphs, including asymptotes, function domains and ranges, graphing, the vertical line test, and the quadratic formula. It also explains trigonometric and circular measures, arc length, sine and cosine rules, and periods. The document further extends into counting and probability with explanations of Pascal’s triangle, conditional and independent events, mutually exclusive events, and estimation concepts like point and interval estimates.",{"@graph":69,"@context":123},[70,84,106],{"@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/mathematical-methods-glossary-unit-1-functions-and-graphs/316232/",{"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/mathematical-methods-glossary-unit-1-functions-and-graphs/316232.png","ImageObject",300,407,{"name":92,"@type":93},"Theodora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does it mean for a line to be an asymptote to a curve?","Question",{"text":113,"@type":114},"A line is an asymptote to a curve if the distance between them approaches zero as they tend to infinity.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you determine whether a relation is a function?",{"text":118,"@type":114},"Use the vertical line test: if every vertical line intersects the graph of the relation in at most one point, it is a function.",{"name":120,"@type":111,"acceptedAnswer":121},"What is a conditional probability?",{"text":122,"@type":114},"Conditional probability describes the probability that an event occurs given that another event has occurred, written using a reduced sample space and expressed as P(A|B).","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},316232,1790877381,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},687197207919,"https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552","Senior Secondary Australian Curriculum  \nMathematical Methods Glossary  \nUnit 1  \nFunctions and graphs  \nAsymptote  \nA line is an asymptote to a curve if the distance between the line and the curve approaches zero as they ‘tend to infinity’. For example, the line with equation ! = !/2 is a vertical asymptote to the graph of ! = tan !, and the line with equation ! = 0 is a horizontal asymptote to the graph of! = 1/! .  \nBinomial distribution  \nThe expansion ! + ! ! = !! + !1 !!!!! + ⋯ + !!  !!!!!! + ⋯ + !! is known as the binomial theorem. The numbers ! =  !!  = !×(!!!)×⋯×(!!!!!) are called binomial coefficients.  \n! !!!!!! !×(!!!)×⋯×!×!  \nCompleting the square  \nThe quadratic expression !!! + !\" + ! can be rewritten as ! ! + !!!! + ! − !!!!~~ ~~  . Rewriting it in this way is called completing the square.  \nDiscriminant  \nThe discriminant of the quadratic expression !!! + !\" + ! is the quantity !! − 4!\"Function  \nA function ! is a rule that associates with each element ! in a set ! a unique element !(!) in a set !. We write ! ⟼ ! (!) to indicate the mapping of ! to !(!) . The set ! is called the domain of ! and the set ! is called the codomain. The subset of ! consisting of all the elements !! : ! ∈ ! is called the range of !. If we write ! = ! (!) we say that ! is the independent variable and ! is the dependent variable.  \nGraph of a function  \nThe graph of a function ! is the set of all points (!, !) in Cartesian plane where ! is in the domain of! and ! = ! !  \nQuadratic formula  \nIf !!! + !\" + ! = 0 with ! ≠ 0, then ! = !!±!!!!~~ ~~!!!\" . This formula for the roots is called the  \nquadratic formula.  \nMathematical Methods Glossary December 2012  \nVertical line test  \nA relation between two real variables ! and ! is a function and ! = ! (!) for some function !, if and only if each vertical line, i.e. each line parallel to the ! − axis, intersects the graph of the relation in at most one point. This test to determine whether a relation is, in fact, a function is known as the vertical line test.  \nTrigonometric functions  \nCircular measure is the measurement of angle size in radians.  \nRadian measure  \nThe radian measure ! of an angle in a sector of a circle is defined by ! = ℓ/!, where ! is the radius and ℓ is the arc length. Thus an angle whose degree measure is 180 has radian measure ! .  \nLength of an arc  \nThe length of an arc in a circle is given by ℓ = !\", where ℓ is the arc length, ! is the radius and ! is the angle subtended at the centre, measured in radians. This is simply a rearrangement of the formula defining the radian measure of an angle.  \nSine rule and cosine rule  \nThe lengths of the sides of a triangle are related to the sines of its angles by the equations  \n! ! !  \n~~ ~~ = ~~ ~~ = ~~ ~~  \nsin! sin ! sin !  \nThis is known as the sine rule.  \nThe lengths of the sides of a triangle are related to the cosine of one of its angles by the equation  \n!! = !! + !! − 2!\" cos !  \nThis is known as the cosine rule.  \nMathematical Methods Glossary December 2012  \nSine and cosine functions  \nIn the unit circle definition of cosine and sine, cos ! and sin ! are the ! and ! coordinates of the point on the unit circle corresponding to the angle !  \nPeriod of a function  \nThe period of a function !! is the smallest positive number ! with the property that !! + ! =! ! for all ! . The functions sin ! and cos ! both have period 2! and tan ! has period !  \nCounting and Probability  \nPascal’s triangle  \nPascal’s triangle is a triangular arrangement of binomial coefficients. The !!! row consists of the binomial coefficients !!  , for 0 ≤ ! ≤ !, each interior entry is the sum of the two entries above it, and sum of the entries in the !!! row is 2!  \nConditional probability  \nThe probability that an event ! occurs can change if it becomes known that another event ! occurs. The new probability is known as a conditional probability and is written as ! !  ! . If ! has occurred, the sample space is reduced by discarding all outcomes th","cbCaihukq8nHR5PE","https://ap.wps.com/l/cbCaihukq8nHR5PE","pdf",10089763,"English","# Asymptote\n# Binomial distribution\n# Completing the square\n# Discriminant\n# Function\n## Graph of a function\n# Quadratic formula\n## Vertical line test\n# Trigonometric functions\n## Radian measure\n## Length of an arc\n## Sine rule and cosine rule\n# Period of a function\n# Counting and Probability\n## Pascal’s triangle\n## Conditional probability\n## Independent events\n## Mutually exclusive\n## Point and interval estimates\n## Relative frequency\n# Unit 2\n## Exponential functions\n## Index laws\n## Arithmetic and Geometric sequences and series","[{\"question\":\"What does it mean for a line to be an asymptote to a curve?\",\"answer\":\"A line is an asymptote to a curve if the distance between them approaches zero as they tend to infinity.\"},{\"question\":\"How do you determine whether a relation is a function?\",\"answer\":\"Use the vertical line test: if every vertical line intersects the graph of the relation in at most one point, it is a function.\"},{\"question\":\"What is a conditional probability?\",\"answer\":\"Conditional probability describes the probability that an event occurs given that another event has occurred, written using a reduced sample space and expressed as P(A|B).\"}]","Mathematical Methods Glossary - Unit 1 - Functions and graphs | PDF",1789911461,25]