{"id":6765,"date":"2014-02-26T18:05:12","date_gmt":"2014-02-26T18:05:12","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6765"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"math-review-of-relations-and-functions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-relations-and-functions\/","title":{"rendered":"Math Review of Relations and Functions"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

While a set of ordered pairs describes a relation, not every relation is also a function.\u00a0 Each x element (the domain) must be paired with only one y element (the range) to be a function.\u00a0\u00a0The relationship between each ordered pair can be tested to determine if the relation is actually a function.<\/p>\n

What Are Ordered Pairs?<\/strong><\/p>\n

Imagine a graph with an x axis and a y axis.\u00a0 Every point on that plane can be described by its coordinates in an ordered pair.\u00a0 Suppose a point has coordinates (3, 1).\u00a0 Its position is 3 units from 0 along the x axis and 1 unit from 0 along the y axis.\u00a0 Another point has coordinates (2, 2).\u00a0 Its coordinates will be 2 units from the x axis and 2 units from the y axis.<\/p>\n

What Is a Relation?<\/strong><\/p>\n

A relation is a set of ordered pairs.\u00a0 For example, one set of ordered pairs might be {(3, 1), (2, 2), (1, 3), (0, 4), (-1, 5), (-2, 6)}.\u00a0 Another relation may be a set of ordered pairs {(0, 5), (0, 2), (3, 1), (2, 2)}.\u00a0 The relation always describes points on the x axis and the y axis.\u00a0 A relation can always be described by its domain and range.\u00a0 The domain of a set of ordered pairs describe the x coordinates.\u00a0 In the first example, the domain would be {3, 2, 1, 0, -1, -2}.\u00a0 The range describes the y coordinates, or (1, 2, 3, 4, 5, 6}.\u00a0 In the second example, the domain would be {0, 3, 2} and the range would be {5, 2, 1, 2}.<\/p>\n

What Is a Function?<\/strong><\/p>\n

In a function, each element in the domain is paired with one element in the range. In the example {(3, 1), (2, 2), (1, 3), (0, 4), (-1, 5), (-2, 6)}the relation is also a function.\u00a0 In the set of ordered pairs {(0, 5), (0, 4), (3, 1), (2, 2)} the relation is not a function because the 0 element in the domain has 2 range values of 5 and 4.\u00a0 Suppose a set of ordered pairs is {(1, 4), (2, 4), (3, 4), (4, 4)}.\u00a0 Although the domain set has the values (1, 2, 3, 4) and the range set has the value (4), it would still be a function.\u00a0 It isn’t a very interesting function because there is only one value in the range, but it is the only value.<\/p>\n

What Is the Vertical Line Test?<\/strong><\/p>\n

Suppose a graph can be plotted of the relationship between 2 variables x and y.\u00a0 If a vertical line can be drawn through that relationship that only intersects it once, the relation is a function.\u00a0 If the vertical line intersects the graph of the relation more than once, then it is not a function.<\/p>\n

Interested in algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Caledonia, ON, Canada: visit Tutoring in Caledonia, ON, Canada<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: While a set of ordered pairs describes a relation, not every relation is also a function.\u00a0 Each x element (the domain) must be paired with only one y element (the range) to be a function.\u00a0\u00a0The relationship between each ordered pair can be tested to determine if the relation is actually a function. What Are […]<\/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":[540,708,1481,1519,2621],"class_list":["post-6765","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-domain","tag-functions","tag-range","tag-relations","tag-vertical-line-test"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6765","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=6765"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6765\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}