10 CHAPTER 1 Graphs Some graphing utilities automatically identify key points such as intercepts and intersection points. For example, Figure 22 shows the graph of = − y x 8 3 using Desmos where the intercepts are already identified. To find the intercepts algebraically requires the ability to solve equations, the subject of the following four sections. The ZERO feature of a TI-84 Plus CE is used to find the x -intercept(s). See Figure 21(c). Rounded to two decimal places, the x -intercept is 2.52. Figure 22 y x 8 3 = − Now Work PROBLEM 55 Figure 21 (c) (b) 10 225 25 5 (a) ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 1.1 Assess Your Understanding 1. On a real number line the origin is assigned the number . (p. A4) 2. On a real number line, graph all numbers x for which < x 5 . (pp. A4–A5) 3. If ( ) x y , are the coordinates of a point P in the xy -plane, then x is called the of P and y is the of P. The coordinate axes divide the xy -plane into four sections called . 4. True or False The point ( ) −1, 4 lies in quadrant IV of the Cartesian plane. Concepts and Vocabulary Skill Building In Problems 7 and 8, plot each point in the xy-plane. Tell in which quadrant or on what coordinate axis each point lies. 7. (a) ( ) = − A 3, 2 (b) ( ) = B 6, 0 (c) C 2, 2 ( ) = − − (d) D 6, 5 ( ) = (e) E 0, 3 ( ) = − (f) F 6, 3 ( ) = − 8. (a) A 1, 4 ( ) = (b) B 3, 4 ( ) = − − (c) C 3, 4 ( ) = − (d) D 4, 1 ( ) = (e) E 0, 1 ( ) = (f) F 3, 0 ( ) = − 9. Plotthepoints 2, 0 , 2, 3 , 2, 4 , 2,1 , ( ) ( ) ( ) ( ) − and 2, 1. ( ) − Describe the set of all points of the form y 2, , ( ) where y is a real number. 10. Plot the points 0, 3 , 1, 3 , 2, 3 , 5, 3 , ( ) ( ) ( ) ( ) − and 4,3 . ( ) − Describe the set of all points of the form x, 3 , ( ) where x is a real number. 5. Multiple Choice Given that the intercepts of a graph are ( ) −4, 0 and ( ) 0, 5 , choose the statement that is true. (a) The y -intercept is −4 and the x -intercept is 5. (b) The y -intercepts are −4 and 5. (c) The x -intercepts are −4 and 5. (d) The x -intercept is −4 and the y -intercept is 5. 6. Multiple Choice Which of the following points does not satisfy the equation − = x y 2 5 20? 2 (a) ( ) − 0, 4 (b) ( ) 5, 6 (c) ( ) − − 5, 14 (d) ( ) 10, 36 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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