{"id":3541,"date":"2013-10-23T16:13:44","date_gmt":"2013-10-23T16:13:44","guid":{"rendered":"http:\/\/testpreparations.com\/help\/?p=3541"},"modified":"2014-12-02T08:26:57","modified_gmt":"2014-12-02T08:26:57","slug":"review-of-math-functions-on-the-sat-and-act","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/10\/23\/review-of-math-functions-on-the-sat-and-act\/","title":{"rendered":"Review of Math Functions on the SAT and ACT"},"content":{"rendered":"

Overview:\u00a0 What Are Functions?<\/strong><\/p>\n

Functions in mathematics describe two different types of relationships between numbers.\u00a0 The simplest definitions are that a function can be either the set of ordered pairs in which the first element is paired with a second element or the relationship between two sets of elements in which every element in Set A can be paired with an unique element in Set B.\u00a0 The definitions are different from each other to reflect the many ways that functions can be represented — as pairs in tables or lists, in rules made up of words, or in graphs.\u00a0 The first elements in the ordered pair or in Set A are the domain or independent variable, represented on the x-axis; and the second elements in the ordered pair or in Set B are the range or dependent variable, represented on the y-axis.<\/p>\n

Linear Functions<\/strong><\/p>\n

Linear functions follow the general form y= mx +b, where m is a constant representing the slope and b is a constant representing the y-intercept (the point at which the line crosses the y-axis).\u00a0 In the real world, most data sets do not follow an exact line, but a line of best fit can be approximated using regression techniques.\u00a0 One common type of linear function used frequently in the social sciences, the correlation coefficient, measures how strongly one variable is related to another.<\/p>\n

Quadratic Functions<\/strong><\/p>\n

Quadratic functions are one type of nonlinear model in which the general form of the equation of best fit follows the quadratic formula ax2<\/sup> + bx +c = 0, where a is not equal to 0, and a, b, and c are all constants.\u00a0 The resulting graph is a parabola.\u00a0 There are many real-world functions that are quadratic, including the Newtonian measurement of the relationship between gravity, velocity, and time.\u00a0 In the equation the variable h represents height the object is initially thrown from, g is the acceleration constant due to gravity, v is velocity, and t is time, so that h=-1\/2gt2<\/sup>-v0<\/sub>t +h0<\/sub>.<\/p>\n

Exponential and Logarithmic Functions<\/strong><\/p>\n

An exponential function occurs when the form of the function f(x) = abx<\/sup>, when a is not equal to 0, b is greater than 0 and not equal to 1.\u00a0 (If b is equal to 1, then the function is linear.)\u00a0 Many different types of exponential functions, such as population growth, occur in the natural world.\u00a0 Logarithmic functions are solved for y rather than x, so they are the inverse.\u00a0 They also form a family of curves.<\/p>\n

Trigonometric Functions<\/strong><\/p>\n

Trigonometric functions include circular functions such as sines, cosines, and tangents, which are derived from the relationships between angles and sides within triangles.\u00a0 As with the graphs of quadratic, exponential, and logarithmic functions, the graphs of trigonometric functions show consistent patterns.\u00a0 The wave patterns illustrate periodic events such as sound and light waves.<\/p>\n

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

Overview:\u00a0 What Are Functions? Functions in mathematics describe two different types of relationships between numbers.\u00a0 The simplest definitions are that a function can be either the set of ordered pairs in which the first element is paired with a second element or the relationship between two sets of elements in which every element in Set […]<\/p>\n","protected":false},"author":6,"featured_media":7811,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2841,3015,3021,2851],"tags":[2691,708,1046,2692,3320],"class_list":["post-3541","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-act","category-math-act","category-mathematics-sat","category-sat","tag-exponential-functions","tag-functions","tag-linear-functions","tag-quadratic-functions","tag-trigonometric-functions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/3541","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=3541"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/3541\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media\/7811"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=3541"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=3541"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=3541"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}