6.10 Functions and Their Graphs 389 Thus, = f (8) 15. Since = f x y ( ) , when = = x y 8, 15. What is the domain and range of = − f x x ( ) 2 1? Because x can be any real number, the domain is the set of real numbers, symbolized .R The range is also .R When looking at a graph, the following test can be used to quickly determine whether the graph represents a function. Definition: Vertical Line Test • If a vertical line can be drawn so that it intersects a graph at more than one point, then the graph does not represent a function. • If a vertical line cannot be drawn so that it intersects a graph at more than one point, then the graph represents a function. Example 2 Using the Vertical Line Test Use the vertical line test to determine which of the graphs in Fig. 6.43 represent functions. a) b) c) d) Figure 6.43 Solution The graphs in parts (a), (b), and (c) represent functions, but the graph in part (d) does not. a) b) c) d) 7 Now try Exercise 25 There are many real-life applications of functions. In fact, all the applications illustrated in Sections 6.1 through 6.3 are functions. In this section, we will discuss three types of functions: linear functions, quadratic functions, and exponential functions. Linear Functions and Their Graphs In Section 6.6, we graphed linear equations. The graph of any linear equation of the form = + y ax b will pass the vertical line test, and so equations of the form = + y ax b are linear functions. If we wished, we could write the linear function as = + f x ax b ( ) . Example 3 Salary as a Linear Function Claudia works at a new vehicle dealership as a sales representative. Claudia’s weekly salary, s, is given by the function = + s x x ( ) 200 0.06 , where x represents Claudia’s weekly sales, in dollars. a) What is Claudia’s weekly salary if during that week she sells one truck for $68,000? b) If for one week, Claudia’s weekly salary was $1580, what were her weekly sales?
RkJQdWJsaXNoZXIy NjM5ODQ=