{"id":100,"date":"2014-01-14t09:00:33","date_gmt":"2014-01-14t09:00:33","guid":{"rendered":"\/\/www.catharsisit.com\/act\/?p=100"},"modified":"2017-09-28t08:56:54","modified_gmt":"2017-09-28t15:56:54","slug":"how-to-make-sense-of-functions-on-the-act-math-test","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/","title":{"rendered":"how to make sense of functions on the act math test"},"content":{"rendered":"

function questions are among the toughest problems you might see on the act math test<\/a>. these questions sometimes ask about domain and range, or present you with a linear or quadratic function and ask you to plug in a number for a variable and solve. functions can also use made-up symbol.<\/p>\n

for these tricky problems, the test maker chooses a completely random symbol, something that you probably haven\u2019t seen before (or at least not in a mathematical context), and give it a new definition<\/i><\/b>.<\/p>\n

you aren\u2019t supposed to already know the meaning of the new symbol in the same way you know common math symbols like +, -, x and \u00f7. the question will tell you exactly<\/i> how the new symbol functions. while these problems may seem intimidating, simple plugging in is usually all that is called for to get the right answer. let\u2019s try an easy one!<\/p>\n

let a \u20ac b be defined by the equation a \u20ac b = a2<\/sup> \u2013 1\/b. what is the value of 3 \u20ac 1?<\/p>\n

(a) 1
\n(b) 3
\n(c) 4
\n(d) 6
\n(e) 8<\/p>\n

here all we have to do is plug in 3 for a and 1 for b to solve.<\/p>\n

\"3^2<\/p>\n

9 \u2013 1 = 8, so the correct answer is (e).<\/p>\n

this same kind of \u201cmonkey see, monkey do\u201d logic can also be applied to non-symbol function questions. let\u2019s try one out:<\/p>\n

if f(x) = 3x \u2013 4 for all real numbers x, what is the value of the function f(x) when four times the value of\u00a0 f(1\/3) is plugged into the input f(x)?<\/p>\n

(f) 50<\/p>\n

(g) 40<\/p>\n

(h) 30<\/p>\n

(j) -40<\/p>\n

(k) -30<\/p>\n

we can translate this wordy question to essentially state: what is f(4(-3))? to solve this one, always start with the innermost parentheses<\/i><\/b>. since 1\/3 is inside of 4, we\u2019ll start by plugging in x = 1\/3 into the function. that gives us f(x) = -3. our question now looks like: what is f(4(-3))? the product of 4 and -3 is -12, so the question now becomes, what is f(-12). we have to plug in -12 into our function again:<\/p>\n

f(x) = 3(-12) -4 = -36 \u2013 4 = -40. the correct answer is (j).<\/p>\n

for function questions, you can also look out for opportunities to use the answer choices to your advantage on symbol function questions! plugging in and working backwards is one act math strategy that really pays off, and the answer choices are a great place to look if you\u2019re feeling stuck!<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

function questions are among the toughest problems you might see on the act math test. these questions sometimes ask about domain and range, or present you with a linear or quadratic function and ask you to plug in a number for a variable and solve. functions can also use made-up symbol. for these tricky problems, […]<\/p>\n","protected":false},"author":97,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[118,9,6],"ppma_author":[24879],"acf":[],"yoast_head":"\nhow to make sense of functions on the act math test - magoosh blog | high school<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"how to make sense of functions on the act math test\" \/>\n<meta property=\"og:description\" content=\"function questions are among the toughest problems you might see on the act math test. these questions sometimes ask about domain and range, or present you with a linear or quadratic function and ask you to plug in a number for a variable and solve. functions can also use made-up symbol. for these tricky problems, […]\" \/>\n<meta property=\"og:url\" content=\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/\" \/>\n<meta property=\"og:site_name\" content=\"magoosh blog | high school\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/magooshsat\/\" \/>\n<meta property=\"article:published_time\" content=\"2014-01-14t09:00:33+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2017-09-28t15:56:54+00:00\" \/>\n<meta name=\"author\" content=\"magoosh act\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:site\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:label1\" content=\"written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"magoosh act\" \/>\n\t<meta name=\"twitter:label2\" content=\"est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"article\",\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/#article\",\"ispartof\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/\"},\"author\":{\"name\":\"magoosh act\",\"@id\":\"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/90c61bb62ffbc6c5d106b40d967ba3a9\"},\"headline\":\"how to make sense of functions on the act math test\",\"datepublished\":\"2014-01-14t09:00:33+00:00\",\"datemodified\":\"2017-09-28t15:56:54+00:00\",\"mainentityofpage\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/\"},\"wordcount\":409,\"commentcount\":0,\"publisher\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/#organization\"},\"keywords\":[\"act functions\",\"act math test\",\"act strategies\"],\"articlesection\":[\"act\"],\"inlanguage\":\"en-us\",\"potentialaction\":[{\"@type\":\"commentaction\",\"name\":\"comment\",\"target\":[\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/#respond\"]}]},{\"@type\":\"webpage\",\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/\",\"url\":\"\/\/www.catharsisit.com\/hs\/act\/how-to-make-sense-of-functions-on-the-act-math-test\/\",\"name\":\"how to make sense of functions on the act math test - 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