Graph of a function

In mathematics, the graph of a function f is the set of ordered pairs, where f = y. In the common case where x and f are real numbers, these pairs are Cartesian coordinates of points in the Euclidean plane and thus form a subset of this plane. In the case of functions of two variables, functions whose domain consists of pairs, the graph is the set of ordered triples where f = z. For a continuous real-valued function of two real variables, the graph is a surface. A graph of a function is a special case of a relation. In science, technology and other areas, graphs are tools used for many purposes. In the simplest case one variable is plotted as a function of another using rectangular axes. In the modern foundations of mathematics, in set theory, a function is equal to its graph. However, it is useful to see functions as mappings, which consist not only of the relation between input and output, but which set is the domain, which set is the codomain. For example, to say; the graph of a function on its own doesn't determine the codomain.

It is common to use both terms function and graph of a function since if considered the same object, they indicate viewing it from a different perspective. Given a mapping f: X → Y, in other words a function f together with its domain X and codomain Y, the graph of the mapping is the set G =,which is a subset of X × Y. In the abstract definition of a function, G is equal to f; the graph of the function f: ↦ defined by f = { a, if x = 1, d, if x = 2, c, if x = 3, is the subset of the set × G =. From the graph, the domain is recovered as the set of first component of each pair in the graph =; the range can be recovered as =. The codomain, cannot be determined from the graph alone; the graph of the cubic polynomial on the real line f = x 3 − 9 x is. If this set is plotted on a Cartesian plane, the result is a curve; the graph of the trigonometric function f = sin ⁡ cos ⁡ is {: x and y are real n

Beverly Daniel Evans Jr.

Beverly Daniel Evans Jr. was a United States District Judge of the United States District Court for the Southern District of Georgia. Born in Sandersville, Evans received an Artium Baccalaureus degree from Mercer University in 1881 and an Artium Magister degree from the same institution in 1882, he was in private practice in Georgia from 1884 to 1894, serving as a member of the Georgia House of Representatives from 1886 to 1887. He was solicitor general of Georgia's Middle Judicial Circuit from 1890 to 1897, he was a judge of the Middle Judicial Circuit of Georgia from 1899 to 1904. He was a Justice of the Supreme Court of Georgia from 1904 to 1917. On August 11, 1917, Evans was nominated by President Woodrow Wilson to a seat on the United States District Court for the Southern District of Georgia vacated by Judge William Wallace Lambdin. Evans was confirmed by the United States Senate on August 15, 1917, received his commission the same day. Evans served in that capacity until his death on May 7, 1922.

Beverly Daniel Evans Jr. at the Biographical Directory of Federal Judges, a public domain publication of the Federal Judicial Center

Members of the Western Australian Legislative Council, 1980–1983

This is a list of members of the Western Australian Legislative Council from 22 May 1980 to 21 May 1983. The chamber had 32 seats made up of 16 provinces each electing two members, on a system of rotation whereby one-half of the members would retire at each triennial election. 1 On 16 December 1981, South Metropolitan Province Labor MLC Howard Olney resigned in order to be appointed to the Supreme Court of Western Australia. Labor candidate Garry Kelly won the resulting by-election on 13 March 1982. 2 On 21 May 1982, North Province MLC Bill Withers, elected as a Liberal but had resigned from the party in May 1981, resigned. Labor candidate Tom Stephens won the resulting by-election on 31 July 1982. Black, David. Legislative Council of Western Australia: membership register, electoral law and statistics, 1890-1989. Perth: Parliamentary History Project. ISBN 0-7309-3641-4. Hughes, Colin A.. Voting for the Australian State Upper Houses, 1890-1984. Canberra: Australian National University. ISBN 0-909779-18-X.

Black, David. "Australian Political Chronicle: July–December 1981". Australian Journal of Politics and History. 28: 115–116. ISSN 0004-9522. Black, David. Biographical Register of Members of the Parliament of Western Australia, Volume Two, 1930-1990. Parliament House: Parliament of Western Australia. ISBN 0731697839