Blog 2

SAT mean scores of college-bound seniors, by race/ethnicity: Selected years, 1986-87 through 2010–11
Year	1986–87	1990–91	1996–97	1999–2000	2000–01	2001–02	2002–03	2003–04	2004–05	2005–06	2006–07	2007–08	2008–09	2009–10	2010–11
SAT- Critical Reading	507	499	505	505	506	504	507	508	508	503	502	502	501	501	497
SAT- Mathematics	501	500	511	514	514	516	519	518	520	518	515	515	515	516	514
SAT- Writing	†	†	†	†	†	†	†	†	†	497	494	494	493	492	489

https://nces.ed.gov/fastfacts/display.asp?id=171

These statistics come from the National Center for Education Statistics. The table above displays the average SAT scores for the corresponding years. The table above represents a function because for every input, of years, there is an output, of scores. However, it is not a linear function as the rate of change is not constant.  It fluctuates yearly either decreasing or increasing meaning that the entire table, should it be graphed, would not have a constant negative or positive slope. This is not a mathematical model because the SAT scores do not depend on the year. Just because the academic year is 2003-2004 does not affect the scores, whereas other factors would.

A function is determined if each input has exactly one output. Therefore in order for a relationship to not be deemed a function there must be more than one output for each corresponding input. An example would be of,  he tide levels on the Potomac river. If the input is one day, say Tuesday, and there are four different readings for Tuesday, then this is not considered a function. If there are four outputs, of different tidal levels, during the one input period of Tuesday, then the information presented is not a function. For Tuesday alone the tide was -0.05 feet and 2.53 feet.

Washington, Potomac River, D.C.
Tuesday	01/21/14	5:16PM	Sunset
Tuesday	01/21/14	6:04PM	-0.05 feet	Low Tide
Tuesday	01/21/14	10:44PM	Moonrise
Tuesday	01/21/14	11:24PM	2.53 feet	High Tide
Wednesday	01/22/14	6:14AM	-0.18 feet	Low Tide
Wednesday	01/22/14	7:21AM	Sunrise
Wednesday	01/22/14	10:25AM	Moonset
Wednesday	01/22/14	11:43AM	2.66 feet	High Tide
Wednesday	01/22/14	5:18PM	Sunset
Wednesday	01/22/14	6:49PM	-0.02 feet	Low Tide
Wednesday	01/22/14	11:44PM	Moonrise
Thursday	01/23/14	6:56AM	-0.17 feet	Low Tide
Thursday	01/23/14	7:21AM	Sunrise
Thursday	01/23/14	10:59AM	Moonset
Thursday	01/23/14	12:10PM	2.48 feet	High Tide
Thursday	01/23/14	12:30PM	2.7 feet	High Tide
Thursday	01/23/14	5:19PM	Sunset
Thursday	01/23/14	7:42PM	0.02 feet	Low Tide

http://www.tides.info/?command=view&location=Washington%2C%20Potomac%20River%2C%20D.C.