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Deep and Wide: Domain & Range TEKS A.2B The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete A function is a set of ordered pairs of numbers (x, y) such that no x –values are repeated. What are the domain and range of a function? The domain and range of a function are sets that describe those ordered pairs. Definition Domain All the x-coordinates in the function's ordered pairs Range All the y-coordinates in the function's ordered pairs Example {(3, 6), (2, 8), (5, 3)} { 3, 2, 5} { 6, 8, 3} The domain is the set of all the values of the independent variable, the xcoordinate The range is the set of all the values of the dependent variable, the ycoordinate. Identify the domain and range of the function below. { 2, 7), (4, 11), (6, 15), (8, 19)} The domain is { 2, 4, 6, 8} The range is { 7, 11, 15, 19} Graphs The domain of a function is the set of all the x-coordinates in the functions’ graph Domain 3 ≤ x ≤ 12 The range of a function is the set of all the ycoordinates in the functions’ graph Range 6 ≤ y ≤ 12 What is the domain of this function? What is the range of this function? Domain is 0 ≤ x ≤ 4 Range is 1 ≤ y ≤ 5 The graph shows the path of a golf ball What is the range of this function? F 0 < y < 100 G 0 ≤ y ≤ 100 H 0≤x≤5 J 0≤x≤5 What is the domain of this function? A -1 ≤ x ≤ 5 B -1 ≤ x ≤ 9 C 2≤x≤5 D 0≤ y≤ 9 What is the domain of the function shown on the graph? A -2 < y ≤ 2 B -4 ≤ x ≤ 6 C -4 < y ≤ 2 D -2 < x ≤ 6 Sometimes you will be asked to determine a REASONABLE domain or range The average daily high temperature for the month of May is represented by the function t = 0.2n + 80 Where n is the date of the month. May has 31 days. What is a reasonable estimate of the domain? Answer: 1 ≤ n ≤ 31 What is a reasonable estimate of the range Answer: See next slide Our function rule is: t = 0.2n + 80 Our domain is 1 ≤ n ≤ 31 Our smallest possible n is 1 Our largest possible n is 31 To find the range, substitute 1 into the equation and solve. Then substitute 31 into the equation and solve. Our function rule is: t = 0.2n + 80 Substitute a 1 t = 0.2n + 80 t = 0.2(1) + 80 t = 0.2 + 80 t = 80.2 Substitute a 31 t = 0.2n + 80 t = 0.2(31) + 80 t = 6.2 + 80 t = 86.2 Reasonable range is 80.2 ≤ t ≤ 86.2