Incorrect Solution Correct Solution and Explanation The domain is -2, ∞) and the range is - ∞). The domain is read from left to right. Since the graph continues indefinitely in the left and right directions, the domain is (-∞, ∞). The range is read from bottom to top and represents the y-values. The bottom-most point is (-2, 0). So, the range is 0, ∞). main ∞ ge 2, ANSWERS TO STUDENT CHECKS Student Check 1 a. {(Nursing, Kaci), (Nursing, Marcus), (Engineering, Andre), (Engineering, Tranh), (Education, Ann), (Education, Mariam), (Biology, Burt), (Biology, Neal), (Business, Bryan)} Domain = {Nursing, Engineering, Education, Biology, Business} Range = {Ann, Andre, Bryan, Burt, Kaci, Mariam, Marcus, Neal, Tranh} b. y = 0.39x, where x is the number of minutes; Domain = {0, 1, 2, 3, 4, 5, . . .}, Range = {0, 0.39, 0.78, 1.17, . . .} c. Domain = {1995, 1996, 1997, 1998, 1999, 2000, 30 28 26 24 22 20 18 16 14 12 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009} Range = {15.9, 16.8, 16.6, 18.3, 19.8, 20.1, 21.1, 22.2, 22.8, 23.2, 24.4, 25.1, 26.3, 26.6, 27.2} Student Check 2 a. Domain = (-∞, ∞), Range = (-∞, ∞) b. Domain = (-∞, ∞), Range = 0, ∞) Student Check 3 a. y = 5 b. x = 1 c. y = 6 d. y = -4 e. y = 4, y = -4 10 1994 1996 1998 2000 2002 2004 2006 2008 2010 SUMMARY OF KEY CONCEPTS 1. A relation is a set of ordered pairs. A relation can be expressed as a set, a mapping, a table, an equation, or a graph. The set of x-values (input values) for the relation is the domain and the set of y-values (output values) is called the range. 2. To determine the domain from a graph, find the interval of x that contains the graph. To determine the range from a graph, find the interval of y that contains the graph. 3. To determine output values for a given input value, find the ordered pair for the relation with the given value as its x-value. The corresponding y-value is the needed output value. If the output value is known, find the ordered pair for the relation with the given value as its y-value. The corresponding x-value is the needed input. GRAPHING CALCULATOR SKILLS The graphing calculator can assist us in fi nding input or output values for a given relation. If the relation is given in terms of an equation solved for y, we can input the equation in the calculator to fi nd the requested information. Example: Find the output value that corresponds to an input value of 0 for the relation y = |x - 4|. Solution: We can do this by using the TABLE feature or the TRACE feature. Input the equation into the calculator. Y= ATH ENTER ENTER X,T,u,n 2 4 ) Method 1: Use the TABLE feature to find the y-value when x = 0. 2nd GRAPH 172 Chapter 3 Graphs, Relations, and Functions
hendricks_intermediate_algebra_1e_ch1_3
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