CCSS STRUCTURE State the domain and range of each relation. Then determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. 1. The left side of the mapping is the domain and the right side is the range.the members of the domain are the x-values of the relation while the members of the range are the y-values. D = { 2, 5, 6}, R = { 8, 1, 3}; Each element of the domain is paired with exactly one element of the range. So, the relation is a function. The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range corresponds to an element of the domain. 2. D = { 2, 1, 4}, R = { 1, 2, 3, 5}; The relation is not a function because 1 is mapped to both 2 and 5. 3. D = { 2, 1, 4, 8}, R = { 4, 2, 6}; Each element of the domain is paired with exactly one element of the range. So, the relation is a function. The function is onto because each element of the range corresponds to an element of the domain. esolutions Manual - Powered by Cognero Page 1
4. BASKETBALL The table shows the average points per game for Dwayne Wade of the Miami Heat for four years. a. Assume that the ages are the domain. Identify the domain and range. b. Write a relation of ordered pairs for the data. c. State whether the relation is discrete or continuous. d. Graph the relation. Is this relation a function? a. Since the ages are the domain, the average points per game are the range. D = {24, 25, 26, 27}, R = {24.6, 27.2, 27.4, 30.2} b. In writing ordered pairs for the relation, the members of the domain are the x-values and the members of the range are the y-values. {(24, 27.2), (25, 27.4), (26, 24.6), (27, 30.2)} c. The domain is a set of individual points. So the relation is discrete. d. The relation is a function as each element of the domain is paired with exactly one element of the range. esolutions Manual - Powered by Cognero Page 2
5. Graph each equation, and determine the domain and range. Determine whether the equation is a function, is one-to-one, onto, both, or neither. Then state whether it is discrete or continuous. To graph the equation, substitute different values of x in the equation and solve for y. Then connect the points. x y = 5x + 4 0 4 1 5 2 14 3 19-1 -1-2 -6-3 -11 D = {all real numbers}; R = {all real numbers}; No vertical line intersects the graph in more than one point. So the graph is a function. The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range corresponds to an element of the domain. The graph of the function is a line. So the function is continuous. esolutions Manual - Powered by Cognero Page 3
6. To graph the equation, substitute different values of x in the equation and solve for y. Then connect the points. x y = -4x - 2 0-2 1-6 2-10 3-14 -1 2-2 6-3 10 D = {all real numbers}; R = {all real numbers}; No vertical line intersects the graph in more than one point. So the graph is a function. The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range correspond to an element of the domain. The domain has an infinite number of elements and the relation can be graphed using a straight line. So the relation is continuous. esolutions Manual - Powered by Cognero Page 4
7. To graph the equation, substitute different values of x in the equation and solve for y. Then connect the points. x y = 3x 2 0 0 1 3 2 12 3 27-1 3-2 12-3 27 D = {all real numbers}; R = {all real numbers}; No vertical line intersects the graph in more than one point. So the graph is a function. The function is neither one-to-one nor onto because the elements in the domain do not have unique images and the negative numbers are left unmapped. The domain has an infinite number of elements and the relation can be graphed using a smooth curve. So the relation is continuous. esolutions Manual - Powered by Cognero Page 5
8. The graph of the equation is a vertical line through (7, 0). In this equation x is always 7 for any value of y. D = {7}; R = {all real numbers}; The only element in the domain is mapped to all the elements in the range. So it is not a function. The domain has a finite number (1) of elements, so the relation is not continuous. esolutions Manual - Powered by Cognero Page 6