M. Pickens ©2006 Domain and Range Part 1

M. Pickens ©2006 Objectives To learn what domain and range areTo learn what domain and range are To determine the domain and range of a table, equation, word problem, set of coordinates.To determine the domain and range of a table, equation, word problem, set of coordinates.

M. Pickens ©2006 Function Machine Input Output IN Out x Y or f(x) Independent Variable Dependent Variable Domain Range

M. Pickens ©2006 What are Domain and Range? DomainDomain The possible values for the independent variable (the possible x values)The possible values for the independent variable (the possible x values) RangeRange The possible values for the dependent variable (the possible y values)The possible values for the dependent variable (the possible y values)

M. Pickens ©2006 Domain and Range of a Table In a table the independent variable is on the ________ and the dependent variable is on the ________.In a table the independent variable is on the ________ and the dependent variable is on the ________. So the values for the domain are on the _________ and the values for the range are on the __________.So the values for the domain are on the _________ and the values for the range are on the __________. left right left right PinksWinks Domain : _______________ Range: _________________ {-2, -1, 0, 1, 2} {4, 6, 8, 10, 12} # of Roses Dollars Domain : _______________ Range: _________________ {1, 2, 3, 4, 5} {5, 10, 15, 20, 25}

M. Pickens ©2006 Domain and Range of an Equation In an equation the __________ variable is by itself. It is what the equation figures out. The ____________ variable is what is plugged into the equation.In an equation the __________ variable is by itself. It is what the equation figures out. The ____________ variable is what is plugged into the equation. Recall: Domain = ___________ Range = _________Recall: Domain = ___________ Range = _________ dependent independent dependent Dependent Independent Domain: All possible values for r Range: All possible values for A Dependent Independent Domain: All possible values for p Range: All possible values for z

M. Pickens ©2006 Domain and Range of a Word Problem James sold CD’s for $5 each after he paid $15 for equipment and supplies. Write an equation showing his profit. Then give the Domain and Range. P = 5c – 15 c = # of CDs sold P = profit Input Output The Domain is all possible c or input values Domain: possible # of CDs sold Domain: whole numbers {0,1,2,3,4….} The Range is all possible P or output values Range: possible profit values Range: {-15, -10, -5, 0, 5, 10, 15, 20…}

M. Pickens ©2006 Domain and Range of a Set of Coordinates What are the domain and range of the following set of coordinates?What are the domain and range of the following set of coordinates? (4, -7), (-3, 9), (2, 0), (7, 4), (-1, 9)(4, -7), (-3, 9), (2, 0), (7, 4), (-1, 9) Domain- all the possible x valuesRange- all the possible y values Domain: {4, -3, 2, 7, -1} Range: {-7, 9, 0, 4}

M. Pickens ©2006 Mixed Practice What are the domain and range of the followingWhat are the domain and range of the following Dependent Independent Domain: All possible values for t Range: All possible values for hTimeHeight Domain : _______________ Range: _________________ {0, 1, 2, 3, 4} {-5, 11, 59, 139, 4091}

M. Pickens ©2006 Mixed Practice Lina’s cell phone company charges her 10 cents per minute plus a $5 service charge each month. She can figure out her bill by the equation C = 0.10m + 5 C = cost m = # of minutes used Give the Domain and Range of the situation (assume the company rounds to the nearest minute) Domain= input= possible # of minutes Domain= whole numbers {0, 1, 2, 3 …} Range= Output= possible cost of bill Range = {$5, $5.10, $5.20, $5.30, $5.40 …}

M. Pickens ©2006 Mixed Practice Give the domain and range of the followingGive the domain and range of the following {(-3, -7), (4, 16), (-0.1, 0), (4, 9), (-2, 3)} Domain: {-3, 4, -0.1, -2} Range: {-7, 16, 0, 9, 3} {(-½, 15), (40, 700), (9.2, 90), (8, -10)} Domain: {-½, 40, 9.2, 8} Range: {15, 700, 90, -10}

M. Pickens ©2006 Mixed Practice What is the domain and range?What is the domain and range? x y List the coordinates (-7, 3), (-4, 6),(-3, -5), (-2, 2), (2, 4), (4, -2), (5, 6) Domain:{-7, -4, -3, -2, 2, 4,5} Range:{3, 6, -5, 2, 4, -2}

M. Pickens ©2006 Mixed Practice If the domain of y = 3x + 4 is {-1, 3, 5} what is the range?If the domain of y = 3x + 4 is {-1, 3, 5} what is the range? If the range of y = 3x + 4 is {-1, 3, 5} what is the domain?If the range of y = 3x + 4 is {-1, 3, 5} what is the domain? x values y values y = 3(-1) + 4 = 1 y = 3(3) + 4= 13 y = 3(5) + 4= 19 Range: {1, 13, 19} y values x values -1 = 3x = 3x 3 3 x = -5/3 3 = 3x = 3x 3 3 x = -1/3 5 = 3x = 3x 3 3 x = 1/3 Domain: {-5/3, -1/3, 1/3}

M. Pickens ©2006 Conclusion Domain is -Domain is - Range is -Range is - The possible values for the independent variable (the possible x values) The possible values for the dependent variable (the possible y values)