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It summarizes interval and set-builder notation, key set operations (union and intersection), and coordinate-plane conventions. It provides distance and midpoint formulas, intercept methods, and graph symmetry rules. It includes function notation essentials (domain and range), transformation steps for shifts, reflections, and scaling, and core line/function concepts such as slope forms. It further covers average rate of change, polynomial behavior at infinity, zero multiplicities, rational-function asymptotes, inverses, radicals, exponents, and logarithm definitions and laws.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/college-algebra-quick-reference-sheet/573099/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/college-algebra-quick-reference-sheet/573099.png","ImageObject",442,249,{"name":88,"@type":89},"Fahsai","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the standard interval notation and set-builder equivalents used in the reference sheet?","Question",{"text":108,"@type":109},"The sheet lists intervals such as (a, b), [a, b], [a, b), (a, b], and rays like (a, ∞), [a, ∞), (-∞, b), and (-∞, b], each matched to a set-builder description of x.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How do transformations of graphs (horizontal/vertical shifts, reflections, and scaling) work?",{"text":113,"@type":109},"Horizontal shift is done by subtracting h from x-coordinates; scaling and possible reflection about the y-axis occur by dividing x-coordinates by b. Vertical scaling and possible reflection about the x-axis occur by multiplying y-coordinates by a, and vertical shifts are made by adding k to y-coordinates.",{"name":115,"@type":106,"acceptedAnswer":116},"What rules does the sheet give for asymptotes of rational functions?",{"text":117,"@type":109},"For vertical asymptotes, if a factor (x-a) is in the denominator but not the numerator, then x=a is a vertical asymptote. For horizontal asymptotes, the location depends on the degrees of the numerator versus denominator; equal degrees give y equal to the ratio of leading coefficients, while lower numerator degree gives y=0.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},573099,1792053430,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":9},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","College Algebra Quick Reference Sheet  \n\n| Set Notation |  |\n| --- | --- |\n| Interval Notation | Set-Builder Notation |\n| (a, b) | { x | a \u003C x \u003C b } |\n| [a, b] | { x | a ≤ x ≤ b } |\n| [a, b) | { x | a ≤ x \u003C b } |\n| (a, b] | { x | a \u003C x ≤ b } |\n| (a, ∞) | { x | a \u003C x } |\n| [a, ∞) | { x | a ≤ x } |\n| (-∞, b) | { x | x \u003C b } |\n| (-∞, b] | { x | x ≤ b } |\n\n\n| Set Operations |  |  |\n| --- | --- | --- |\n| Operation | Elements | Logic |\n| Union | All | OR |\n| Intersection | Common | AND |\n\n\n| Coordinate Plane Quadrants |  |\n| --- | --- |\n| II | I |\n| III | IV |\n\n\n| Distance and Midpoint Formulas |\n| --- |\n| If P1=(x1,y1) and P2=(x2,y2) are two points, the distance between them is |\n| and the midpoint coordinates are |\n\n\n| Intercepts of an Equation |  |\n| --- | --- |\n| x-intercepts | Set y = 0; solve for x |\n| y-intercepts | Set x = 0; solve for y |\n\n\n| Symmetry of the Graph of an Equation |  |  |\n| --- | --- | --- |\n| Type | Mathematical | Geometrical |\n| x-axis | Unchanged when\u003Cbr>y replaced by-y | Unchanged when\u003Cbr>reflected about\u003Cbr>x-axis |\n| y-axis | Unchanged when\u003Cbr>x replaced by-x | Unchanged when\u003Cbr>reflected about\u003Cbr>y-axis |\n| origin | Unchanged when\u003Cbr>y replaced by –y &\u003Cbr>x replaced by-x | Unchanged when\u003Cbr>rotated 180°\u003Cbr>about origin |\n\n\n| Function Notation y = f(x) |  |\n| --- | --- |\n| Domain | Set of all valid x |\n| Range | Set of all valid y |\n\n\n| Function Arithmetic |\n| --- |\n|  |\n|  |\n|  |\n|  |\n\n\n| Transformations of Graphs of Functions |\n| --- |\n| Horizontal Vertical Shift (left)\u003Cbr>(right) (up)\u003Cbr>(down) Reflect (y-axis) (x-axis) Scale (compress) (expand)\u003Cbr>1. Subtract h from each ofthe x-coordinates of the points on the graph off. This results in a horizontal shift to the left if h > 0 (positive h) or right if h \u003C 0 (negative h) .\u003Cbr>2. Divide the x-coordinates of the points on the graph obtained in Step 1 by b. This results in a horizontal scaling, but may also include a reflection about the y-axis if b \u003C 0 (negative b) .\u003Cbr>3. Multiply the y-coordinates of the points on the graph obtained in Step 2 by a. This results ina vertical scaling, but may also include a reflection about the x-axis ifa \u003C 0 (negative a) .\u003Cbr>4. Add k to each of the y-coordinates of the points on the graph obtained in Step 3. This results in a vertical shift up ifk > 0 (positive k) or down ifk \u003C 0 (negative k) . |\n\n\n| Properties of Equality |\n| --- |\n|  |\n|  |\n\n\n| Properties of Inequalities |\n| --- |\n|  |\n|  |\n|  |\n\n\n| Lines or Linear Functions |\n| --- |\n| Slope of Line through points (x1, y1) & (x2, y2) |\n| Slope-Intercept Form-slope m and point (0, b) |\n| Point-Slope Form-slope m and point (x1, y1) or |\n| Horizontal Line through point (0, b) |\n| Vertical Line through point (a, 0) |\n\n\n| Average Rate of Change |\n| --- |\n| The average rate of change m for function y=f(x) between x=a and x=b is |\n\n\n| Absolute Value Properties |  |\n| --- | --- |\n|  |  |\n|  |  |\n|  |  |\n\n\n| Absolute Value Function as a Piecewise-Defined Function |\n| --- |\n|  |\n\n\n| Absolute Value Equations and Inequalities |\n| --- |\n| If c is a positive number: |\n|  |\n|  |\n|  |\n|  |\n|  |\n\n\n| Parabolas or Quadratic Functions |\n| --- |\n| General Form\u003Cbr>The graph has a smile if a is positive and a frown if a is negative, and has a vertex at coordinates: |\n| Vertex Form\u003Cbr>The graph has a smile if a is positive and a frown if a is negative, and has a vertex at (h, k) . |\n\n\n| Special Factoring Formulas |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n\n\n| Special Product Formulas |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n\n\n| Quadratic Formula |\n| --- |\n| Solve |\n|  |\n| If , then 2 real unequal solutions |\n| If , then 2 real duplicate solutions |\n| If , then no real solutions |\n| Factored Form for real factors: |\n\nPage 1  \nCollege Algebra Quick Reference Sheet  \n\n| End Behavior of a Polynomial Function |  |  |\n| --- | --- | --- |\n| n | a | Behavior |\n| odd |  |  |\n| odd |  |  |\n| even |  |  |\n| even |  |  |\n\n\n| Multiplicities of Real Zeros of a Polynomial Function |  |\n| --- | --- |\n| m | Behavi","cbCaiuraHzESXPaC","https://ap.wps.com/l/cbCaiuraHzESXPaC","pdf",508776,"English","# Set Notation\n## Interval and Set-Builder Notation\n# Set Operations\n## Union and Intersection\n# Coordinate Plane and Symmetry\n## Quadrants\n## Symmetry Rules\n# Function Essentials\n## Function Notation (Domain and Range)\n## Transformations of Graphs\n# Lines and Rates of Change\n## Slope Forms\n## Average Rate of Change\n# Polynomials and Rational Functions\n## End Behavior and Multiplicity\n## Rational Function Asymptotes\n# Inverses, Radicals, Exponents, and Logarithms\n## Inverse Functions\n## Radical and Exponent Properties\n## Logarithm Definition and Laws","[{\"question\":\"What are the standard interval notation and set-builder equivalents used in the reference sheet?\",\"answer\":\"The sheet lists intervals such as (a, b), [a, b], [a, b), (a, b], and rays like (a, ∞), [a, ∞), (-∞, b), and (-∞, b], each matched to a set-builder description of x.\"},{\"question\":\"How do transformations of graphs (horizontal/vertical shifts, reflections, and scaling) work?\",\"answer\":\"Horizontal shift is done by subtracting h from x-coordinates; scaling and possible reflection about the y-axis occur by dividing x-coordinates by b. Vertical scaling and possible reflection about the x-axis occur by multiplying y-coordinates by a, and vertical shifts are made by adding k to y-coordinates.\"},{\"question\":\"What rules does the sheet give for asymptotes of rational functions?\",\"answer\":\"For vertical asymptotes, if a factor (x-a) is in the denominator but not the numerator, then x=a is a vertical asymptote. For horizontal asymptotes, the location depends on the degrees of the numerator versus denominator; equal degrees give y equal to the ratio of leading coefficients, while lower numerator degree gives y=0.\"}]","College Algebra Quick Reference Sheet | PDF",1791932213]