{"id":7021,"date":"2014-05-05T18:01:26","date_gmt":"2014-05-05T18:01:26","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=7021"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-functions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-functions\/","title":{"rendered":"Math Review of Functions"},"content":{"rendered":"

Overview:<\/h3>\n

In a mathematical function, each value of x (the domain) can be matched with only one value of y (the range).\u00a0 If there is one value for x, but multiple values of y, the relationship is not a function, but a relation.\u00a0 Many different types of functions can be described by plotting the values of x and y on a coordinate plane.\u00a0 Functions can be described graphically, by their equation, by listing a finite number of ordered pairs, or by listing their defining rule.<\/p>\n

Functions and Relations<\/h3>\n

When ordered pairs are graphed in a function, one value of x can be matched with one value of y.\u00a0 Suppose the set of ordered pairs is {(3, 5), (4, 6), (5, 7), (6, 8), (7, 9) \u2026}.\u00a0 It is a function, because the value of x predicts the value of y.\u00a0 Similarly, suppose the set of ordered pairs is {(3, 2), (4, 2) (5, 2), (6, 2) \u2026}.\u00a0 It is also a function, because the value of x is also matched with one value of y.\u00a0 It isn\u2019t a very interesting function.\u00a0 However, if the set of ordered pairs is {(3,2), (3,3), (3,4), (1,2), (2,2), (4,3)} it is not a function, but a relation.\u00a0 The x-value of 3 has 3 different y-values. There are sets of ordered pairs, but they do not describe unique relationships between values of x and values of y.<\/p>\n

Linear Functions<\/h3>\n

Equations that have the form y=mx + b (the slope-intercept form) have one x for one y, and are called linear functions.\u00a0 A simple equation such as y=x is a linear function, as is 2x = y, and so is 2y = 4x + 20.\u00a0 When a line is fit to data, the line itself is a function (even if the raw data from the scatterplot describes a relation).<\/p>\n\n\n\n
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Figure 2:\u00a0 The raw data from the scatterplot describes a relation, but the line of best fit is a linear function.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

 <\/p>\n

Exponential Functions<\/h3>\n

Like linear functions, exponential functions of growth or decay have values of x that correspond to values of y.\u00a0 The graph of an exponential function is a curved line.\u00a0 Suppose that $100.00 is invested at 6% compound interest.\u00a0 Compound interest is an example of exponential growth.\u00a0 In this case, the equation is y = 100(1.06)x<\/sup>, where x is the number of years and y is the amount saved.\u00a0 The values in ordered pairs are {(0, 100), (5, 134), (10, 179), (15, 240), (20, 321), (25, 429), (30, 574)}.\u00a0 There are many real-life examples of exponential functions besides compound interest, such as many forms of biological growth and decay.<\/p>\n\n\n\n
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Figure 3: Exponential functions still show the relationship between values on x and values of y.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

\u00a0<\/strong><\/span><\/p>\n

Quadratic Functions<\/h3>\n

Quadratic equations, such as y = ax2<\/sup> + bx + c, take the form of a parabola when they are graphed.\u00a0 The parabola for an equation of this form is vertical.\u00a0 If the coefficient for a is positive, the parabola opens up, and if the coefficient for a is negative, the parabola opens down.\u00a0 There are many real world examples of parabolas, including the path of a tossed ball, the spray of water in a fountain, and the path of a cliff diver.<\/p>\n\n\n\n
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Figure 4:\u00a0 Quadratic functions take the shape of a parabola.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

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Overview: In a mathematical function, each value of x (the domain) can be matched with only one value of y (the range).\u00a0 If there is one value for x, but multiple values of y, the relationship is not a function, but a relation.\u00a0 Many different types of functions can be described by plotting the values […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2691,1046,2692,1519],"class_list":["post-7021","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-exponential-functions","tag-linear-functions","tag-quadratic-functions","tag-relations"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=7021"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7021\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}