316 CHAPTER 2 Graphs and Functions 11. (3, 5) x y 0 12. (–2, 3) x y 0 13. (–2, 6) (0, 3) x y 0 14. (4, 9) (5, 6) x y 0 Concepts Examples Composition of Functions If ƒ and g are functions, then the composite function, or composition, of ƒ and g is defined by 1 ƒ° g2 1x2 =ƒ1g1x2 2. The domain of ƒ∘ g is the set of all x in the domain of g such that g1x2 is in the domain of ƒ. Let ƒ1x2 = 2x - 4 and g1x2 = 2x. Find 1ƒ∘ g21x2. 1ƒ∘ g21x2 = 22x - 4 The domain is all x such that x Ú 0, represented by the interval 30, ∞2. Chapter 2 Review Exercises Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. 1. P13, -12, Q1-4, 52 2. M1-8, 22, N13, -72 3. A1-6, 32, B1-6, 82 4. Are the points 15, 72, 13, 92, and 16, 82 the vertices of a right triangle? If so, at what point is the right angle? 5. Determine the coordinates of B for line segment AB, given that A has coordinates 1-6, 102 and the coordinates of its midpoint M are 18, 22. 6. Use the distance formula to determine whether the points 1-2, -52, 11, 72, and 13, 152 are collinear. Find the center-radius form of the equation of each circle. 7. center 1-2, 32, radius 15 8. center A 25, -27B, radius 23 9. center 1-8, 12, passing through 10, 162 10. center 13, -62, tangent to the x-axis Connecting Graphs with Equations Use each graph to determine an equation of the circle. Express it in center-radius form.
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