246 CHAPTER 2 Graphs and Functions ALGEBRAIC SOLUTION (d) To make a profit, P1x2 must be positive. P1x2 = 25x - 1500 Profit function from part (c) Set P1x2 70 and solve. P1x2 70 2 5x - 1500 70 P1x2 = 25x - 1500 25x 71500 Add 1500 to each side. x 760 Divide by 25. The number of items must be a whole number, so at least 61 items must be sold for the company to make a profit. GRAPHING CALCULATOR SOLUTION (d) Define y1 as 25x - 1500 and graph the line. Use the capability of a calculator to locate the x-intercept. See Figure 44. As the graph shows, y-values for x less than 60 are negative, and y-values for x greater than 60 are positive, so at least 61 items must be sold for the company to make a profit. y1 = 25x−1500 −500 0 1500 100 Figure 44 S Now Try Exercise 81. CAUTION In problems involving R1x2 - C1x2, such as Example 10(c), pay attention to the use of parentheses around the expression for C1x2. 2.4 Exercises CONCEPT PREVIEW Match the description in Column I with the correct response in Column II. Some choices may not be used. II A. ƒ1x2 = 5x B. ƒ1x2 = 3x + 6 C. ƒ1x2 = -8 D. ƒ1x2 = x2 E. x + y = -6 F. ƒ1x2 = 3x + 4 G. 2x - y = -4 H. x = 9 I 1. a linear function whose graph has y-intercept 10, 62 2. a vertical line 3. a constant function 4. a linear function whose graph has x-intercept 1-2, 02 and y-intercept 10, 42 5. a linear function whose graph passes through the origin 6. a function that is not linear CONCEPT PREVIEW For each given slope, identify the line in A–D that could have this slope. 7. -3 8. 0 9. 3 10. undefined B. 0 x y C. 0 x y D. 0 x y 0 x y A.
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