{"id":8635,"date":"2015-07-26T22:59:11","date_gmt":"2015-07-26T22:59:11","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8635"},"modified":"2015-07-26T22:59:11","modified_gmt":"2015-07-26T22:59:11","slug":"math-review-of-writing-and-graphing-functions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2015\/07\/26\/math-review-of-writing-and-graphing-functions\/","title":{"rendered":"Math Review of Writing and Graphing Functions"},"content":{"rendered":"

Overview<\/h3>\n

A function is a special relationship between variables in an equation such that for every domain value, there is only one range value. Functions can be expressed using a function rule that defines those values. Once enough values have been derived, the function can be graphed.<\/p>\n

Independent and Dependent Variables<\/h3>\n

In order to begin thinking about writing a function, first determine how the variables are related. Does the value of one variable depend upon the value of another? Suppose a plumber charges $75.00 per hour plus a labor charge of $50.00. The cost of the repair depends upon the number of hours it takes. Therefore, if the repair takes 1 hour, the cost of the repair is $125.00, and if it takes 2 hours, the cost is $200.00, and so on. Another way to say that is that the cost of the repair is the dependent variable, and the number of hours is the independent variable. Suppose that a car gets 30 miles to the gallon. The number of gallons used depends upon the number of miles driven. If the car is driven 30 miles, it uses one gallon; 60 miles, 2 gallons; and so on.<\/p>\n

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Function Notation and Function Rule<\/h3>\n

After the independent and dependent variables have been identified, the next step is to write an equation. In the plumbing example, y, the cost of the repair, equals $75.00x + $50.00, where x is the number of hours. Since $75.00x + $50 defines the function, it is the function rule. Similarly, the number of gallons used, y, equals the number of miles driven, x, divided by 30. The function rule of x\/30 defines the function. Function notation is substituted for the dependent variable y, so that f(x) = $75.00x + $50.00, or f(x) =x\/30. Functions are usually represented with the letters f, g, or h, so they may be expressed as f(x), g(x), or h(x).<\/p>\n

Organizing a Table<\/h3>\n

The first step to graphing a function is to organize a table with values of x and y. It is better to use many values to show a pattern. Suppose that the function is a simple one, such as f(x) = 10x. Then if x =1, f(x) = 10; if x=2, f(x) = 20, x =3, f(x) =30, and so on. If the domain of a function is given in a problem as specific values of x, only use those values, but if it is not specified, the domain is all real numbers.<\/p>\n

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Graphing a Function<\/h3>\n

After the table with values of x and y is generated, points can be plotted using Cartesian coordinates. Once the pattern is established, a line or smooth curve can be drawn through them. If the domain of x is all real numbers, the endpoints of the line can be drawn as arrowheads.<\/p>\n

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Overview A function is a special relationship between variables in an equation such that for every domain value, there is only one range value. Functions can be expressed using a function rule that defines those values. Once enough values have been derived, the function can be graphed. Independent and Dependent Variables In order to begin […]<\/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":[3798,3799,3800,930],"class_list":["post-8635","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-dependent-variable","tag-function-rule","tag-graphing-functions","tag-independent-variable"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8635","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=8635"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8635\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}