[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-267424-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-267424-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","sat-math-function-quiz","SAT Math Function Quiz","","Practice set focused on SAT-style function questions, emphasizing substitution into algebraic expressions, evaluating function values at specific inputs, and combining outputs. Includes inverse-thinking items where a given function output is used to solve for the input variable, plus composition-style evaluation such as f(a+b). Problems also feature solving when inputs appear inside parentheses and using a provided graph to read function values and compute f(2k).",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/sat-math-function-quiz/267424/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/sat-math-function-quiz/267424.png","ImageObject",300,407,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do these problems typically evaluate functions at given values?","Question",{"text":63,"@type":64},"They substitute the provided input for the variable inside the function definition, then compute the resulting expression to get the function value.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What does it mean when a question asks to solve for the input from a given function output?",{"text":68,"@type":64},"It works backwards: the problem provides a function output such as h(a)=27, so you set the expression equal to the given output and solve for the variable a.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the graph-based function question solved?",{"text":72,"@type":64},"You read f(x) from the graph by locating the x-value, identifying the corresponding y-value, then use that value (like k) to compute the requested output f(2k).","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},267424,1789418451,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":111},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","SAT Math Function Quiz  \n1. If f(x) = 2x 􀀀 5, then what is the value of f (2) + f (5) ?  \n(A) 1  \n(B) 2  \n(C) 3  \n(D) 4  \n(E) 5  \n2. If h (x) = 3x + 5 and h (a) = 27, then what is the value of a ?  \n3. Let f (x) = 4x 􀀀 3. If f (a) = 9 and f (b) = 5, then what is f (a + b) ?  \n(A) 5  \n(B) 7  \n(C) 14  \n(D) 16  \n(E) 17  \n4. If f (x) = x2 􀀀 1, and f (2a) = 35, then what could be the value of a ?  \n(A) 􀀀6  \n(B) 􀀀3 (C) 1 (D) 2 (E) 6  \n5. If f(x) = 2x +4, then what is the value of f (4) + f (6) ?  \n(A) f (8)  \n(B) f (10)  \n(C) f (12)  \n(D) f (18)  \n(E) f (28)  \nz (q) = 4q + 12  \n6. The zoomster function z used in space  \n􀀍ight engineering is de􀀌ned above. If, for some number u, z (u + 1/2) = 1/2, then what is the value of u ?  \n(A) 􀀀3/2  \n(B) 􀀀1/2  \n(C) 􀀀1/8  \n(D) 1/8  \n(E) 1/2  \n7. For any positive integer n, let n♥ bede􀀌ned by n♥ = 2n(n +1) . What is the  \n8♥ value of 2♥ ?  \n(A) 2♥  \n(B) 4♥  \n(C) 6♥  \n(D) 8♥  \n(E) 10♥  \ny  \n2 ~~ ~~  \n 1  f (x)  \nx 􀀀2 􀀀1 ~~ ~~ 1 2  \n8. For the function f graphed in the xyplane above, if f(􀀀2 .5) = k, then what is f (2k) ?  \n[www.erikthered.com/tutor](www.erikthered.com/tutor)  \nSAT Math Function Quiz  \nAnswers  \n1. D  \nFirst, 􀀌nd f (2) by plugging in 2 for x in the expression 2x 􀀀 5. We get f (2) = 2􀀁2􀀀5 = 4􀀀5 = 􀀀1 . Similarly, f (5) = 2􀀁5􀀀5 = 5 . Then, f (2)+f (5) = 􀀀1+5 = 4, so answer D is correct.  \n2. 22/3 or 7 .33  \nFirst, 􀀌nd h (a) . Whatever is inside the parentheses of a function gets substituted for x in the given expression for the function. So here, h (a) = 3a + 5 . Since h (a) = 27, we have 3a + 5 = 27, so that 3a = 22 and a = 22/3 (or a = 7 .33) .  \nThis question is typical on the SAT and ACT; it is asking us to go “backwards”. Suppose that y = h (x) . Instead of giving us x and asking us for y, it is giving us y and asking us for x. Also, don’t be fooled by the use of the di􀀋erent letters (h instead of f for the function, and a instead of x); the math is the same.  \n3. E  \nSince f (a) = 4a 􀀀 3 and f (a) = 9, then 4a 􀀀 3 = 9 so that 4a = 12 and a = 3 . Similarly, f (b) = 4b 􀀀 3 = 5 so that 4b = 8 and b = 2 . Finally, f (a +b) = f (3+2) = f (5) = 4 􀀁 5 􀀀 3 = 17 . Answer E is correct.  \n4. B  \nWe substitute the 2a inside the function parentheses for x in the expression x2 􀀀 1. This gives f (2a) = (2a)2 􀀀 1 = 4a2 􀀀 1. Since f (2a) = 35, we have 4a2 􀀀 1 = 35, so that 4a2 = 36, or a2 = 9 . Solving for a gives a = 􀀆3, and answer B is correct. Note that since there can be only one answer, 3 is not given as an answer choice.  \nIn this case, don’t forget to substitute everything inside the parentheses into x. A common mistake here is to square the a but not the 2, resulting in the expression 2a2 􀀀 1 = 35, which is incorrect.  \n5. C  \nSince f (4) = 2(4)+4 = 12, and f (6) = 2(6)+4 = 16, then f (4)+f (6) = 12+16 = 28 . To 􀀌gure out which answer is correct, we have to evaluate each one until we get 28 as the value. Since f (12) = 2(12) + 4 = 28, answer C is correct.  \npg. 2 [www.erikthered.com/tutor](www.erikthered.com/tutor)  \nSAT Math Function Quiz  \n6. B  \nTo evaluate z (u + 1/2), we need to substitute everything inside the parentheses into q, i.e., we substitute u + 1/2 for q in the de􀀌nition of the function z. We get: z (u + 1/2) = 4(u + 1/2) + 1/2 = 4u + 2 + 1/2 = 4u + 5/2 . Since z (u + 1/2) = 1/2, this means that 4u + 5/2 = 1/2 . Solving for u, we get 4u = 􀀀2, or u = 􀀀1/2.  \n7. A  \nThis question is an example of what I call “wacky functions”. These are functions in the disguise of weird symbols that you probably have never seen in math class before. That is because the symbols are completely made up! The question will always tell you exactly what the symbol means. In this case, we are told that n♥ = 2n(n + 1) . This means, for example, that 8♥ = 2 􀀁 8 􀀁 (8 + 1) = 2 􀀁 8 􀀁 9 = 144 . Similarly, 2♥ = 2 􀀁 2 􀀁 (2 + 1) = 2 􀀁 2 􀀁 3 = 12 . Therefore, 8♥ /2♥ = 144/12 = 12 . Since 2♥ = 12, choice A is correct.  \nNote that this question is identical to the following “regular” function question:  \nFor an","cbCaivR9oKDK7S0D","https://ap.wps.com/l/cbCaivR9oKDK7S0D","pdf",41089,"English","# SAT Math Function Quiz\n## Questions 1-8\n## Answers and explanations","[{\"question\":\"How do these problems typically evaluate functions at given values?\",\"answer\":\"They substitute the provided input for the variable inside the function definition, then compute the resulting expression to get the function value.\"},{\"question\":\"What does it mean when a question asks to solve for the input from a given function output?\",\"answer\":\"It works backwards: the problem provides a function output such as h(a)=27, so you set the expression equal to the given output and solve for the variable a.\"},{\"question\":\"How is the graph-based function question solved?\",\"answer\":\"You read f(x) from the graph by locating the x-value, identifying the corresponding y-value, then use that value (like k) to compute the requested output f(2k).\"}]","SAT Math Function Quiz | PDF"]