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MAT091 :: Lecture Note :: Week 09
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The inputs and outputs of a function are often represented as ordered pairs (or points).
(input, output) ...or... (x, y) ...or... (x, f(x)) (t, n) ...or... (t, f(t)) (n, o) ...or... (n, f(n)) (a, b) ...or... (a, f(a))The input is always the first value recorded followed by its respective output.
Data contained in tables can sometimes be represented as orderedpairs.
input: month ......... output: #days month  1  2  3  4  5  6  7  8  9  10  11  12  #days  31  28  31  30  31  30  31  31  30  31  30  31 (1, 31) (2, 28) (3, 31) (4, 30) (5, 31) (6, 30) (7, 31) (8, 31) (9, 30) (10, 31) (11,30) (12, 31) #days depends on the month (i.e. the output depends on the input) The function f(m) takes a month as input and outputs the number of days in that month. f(m) = n f(1) = 31 f(2) = 28 f(7) = 31 f(12) = 31Orderedpairs are points that can be graphed. The input is along the horizontalaxis and output is along the verticalaxis.
The following orderedpairs could represent a function because all of the inputs are unique (i.e. different).
(2, 3) (0, 4) (5, 2) (7, 4) (11, 7)The following orderedpairs could represent a function because all of the inputs are unique although some of the inputs repeat.
(2, 3) (0, 4) (5, 2) (7, 4) (11, 7) (0, 4)The following orderedpairs cannot be a function because input 3 produces different outputs (2 and 5).
(2, 3) (0, 4) (2, 3) (3, 2) (0, 4) (3, 5)
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When it comes to graphing functions, tables and other forms of data, input values are scaled along the horizontalaxis and output values are scaled along the verticalaxis.
When it comes to naming variables, the letter
x
is often used to represent the input variable and the lettery
is used to represent the output variable; however, any letters can be used when it comes to naming input and output variables.Table A =============================================================== input: year (y)  2001  2002  2003  2004  2005  2007  output: # xrays (x)  55 43 81 24 43 61 The # of xrays is a function of the year; i.e. year is the input and # of xrays is the output. For this function, the input variable is named 'y' and the output variable is named 'x'. Table A expressed using function notation. f(y) = x f(2001) = 55 f(2002) = 43 f(2003) = 81 ... f(2000) = undefined [cannot extrapolate] f(2006) = undefined [cannot interpolate] Table B ============================================================== input: hours (h)  1  2  3  4  5  6  7  output: minutes (m)  60  120  180  240  300  360  420 Number of minutes is a function of number of hours. One hour is 60 minutes, two hours is 120 minutes, etc. Table B expressed using function notation. g(h) = m = 60(h) g(1) = 60 g(4) = 240 g(7) = 420 g(2.5) = 150 [interpolation] g(5.25) = 315 [interpolation] g(0) = 0 [extrapolation] g(8) = 480 [extrapolation]
[definition]
A function is a "relation for which each element of the domain corresponds to exactly one element of the range."
{PurpleMath}
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{KhanAcademy}
{UdacityMOOC}
{OpenAlgebra}
{InteractiveMathematics}
{TIcalculatorHelp}
{SCC math resources... MathAS::id 6433, key 6433 
OER::textbook 
playbook}
{TopOfPage}
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thinking 
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