7b. Write the linear equation x = 5 in function notation. �������������������������������������� ���������������������������������������������������������������� The equation x = 5 in function The equation x = 5 is a vertical line and is not notation is f x) 5. a function. It cannot be written in function notation. 7c. If f (x) = 7x + 9, find f (2). �������������������������������������� ���������������������������������������������������������������� f (2) = (7x + 9)(2) = 14x + 18 The notation f (2) means to evaluate the function at x = 2. It does not mean multiplication. f (2) = 7(2) + 9 = 14 + 9 = 23 n x 5 f ( ) = 5 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 = 0.39; Domain = {0, 1, 2, 3, . . .}, Range = {0, 0.39, 0.78, 1.17, . . .} Domain = {1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009} Range = {15.9, 16.6, 16.8, 18.3, 19.8, 20.1, 21.1, 22.2, 22.8, 23.2, 24.4, 25.1, 26.3, 26.6, 27.2} 30 28 26 24 22 20 18 16 14 12 10 1994 1996 1998 2000 2002 2004 2006 2008 2010 Student Check 2 a. no, the x-value of 5 corresponds to more than one y-value. b. yes c. yes d. yes Student Check 3 a. yes b. yes c. no d. yes Student Check 4 a. f (0) = 4 b. g(-5) = -29 c. c(2) = -6 d. f (-2) = 0 Student Check 5 a. f (x)=- 2 3 x + 2; f (0) = 2; f (3) = 0; f (-2) = 10 3 b. f (x) = 1; f (0) = 1; f (3) = 1; f (-2) = 1 Student Check 6 521.29 million cell phone subscribers. SUMMARY OF KEY CONCEPTS 1. A relation is a set of ordered pairs. The set of x-values of the ordered pairs is the domain. The set of y-values of the ordered pairs is the range. 2. A function is a relation in which each input has only one output, that is, for every x in the domain of the function, there is exactly one y-value. The x-values in the list of ordered pairs cannot repeat for the relation to be a function. 3. The vertical line test can be used to determine if a graph represents a function. If any vertical line intersects a graph in more than one point, the graph does not represent a function. 4. Function notation, f (x), is another name for the output value y. It shows that y is dependent on the value of x. When a specific value of x is inside the function notation, we evaluate the function at that value. 274 Chapter 3 Linear Equations in Two Variables
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