252 CHAPTER 2 Graphs and Functions 91. Find the distance between the second and fourth points in the table. 92. Find the distance between the first and fourth points in the table. 93. Add the results in Exercises 90 and 91, and compare the sum to the answer found in Exercise 92. What do you notice? 94. Fill in each blank, basing the answers on observations in Exercises 90–93: If points A, B, and C lie on a line in that order, then the distance between A and B added to the distance between and is equal to the distance between and . 95. Find the midpoint of the segment joining 10, -62 and 16, 122. Compare the answer to the middle entry in the table. What do you notice? 96. If the table were set up to show an x-value of 4.5, what would be the corresponding y-value? Chapter 2 Quiz (Sections 2.1–2.4) 1. For A1-4, 22 and B1-8, -32, find d1A, B2, the distance between A and B. 2. Two-Year College Enrollment Enrollments in two-year colleges for selected years are shown in the table. Use the midpoint formula to estimate the enrollments for 2010 and 2014. 3. Graph y = -x2 + 4 by plotting points. 4. Graph x2 + y2 = 16. 5. Determine the radius and the coordinates of the center of the circle with equation x2 + y2 - 4x + 8y + 3 = 0. For Exercises 6–8, refer to the graph of ƒ1x2 = 0 x + 30 . 6. Find ƒ1-12. 7. Give the domain and the range of ƒ. 8. Give the largest open interval over which the function ƒ is (a) decreasing, (b) increasing, (c) constant. 9. Find the slope of the line through the given points. (a) 11, 52 and 15, 112 (b) 1-7, 42 and 1-1, 42 (c) 16, 122 and 16, -42 10. (Modeling) Spread of a Rumor A rumor is spreading by word of mouth through a town. The number of people who have heard the rumor after t days is shown in the graph. Find the average rate of change, to the nearest person, of the spread of the rumor from day 14 to day 24. People Time (in days) Spread of a Rumor 0 10 30 100,000 y t 60,000 40,000 20,000 15 20 25 5 80,000 (24, 95,865) (14, 71,341) y = f(t) Year Enrollment (in millions) 2008 6.97 2012 7.17 2016 6.09 Data from National Center for Education Statistics. (–3, 0) (–1, 2) (–5, 2) 0 f(x) = z x+ 3z x y
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