322 CHAPTER 2 Graphs and Functions 10. Suppose point A has coordinates 15, -32. What is the equation of the (a) vertical line through A? (b) horizontal line through A? 11. Find the slope-intercept form of the equation of the line passing through 12, 32 and (a) parallel to the graph of y = -3x + 2 (b) perpendicular to the graph of y = -3x + 2. 12. Consider the graph of the function shown here. Give the open interval(s) over which the function is (a) increasing (b) decreasing (c) constant (d) continuous. (e) What is the domain of this function? (f) What is the range of this function? Graph each function. 13. ƒ1x2 = x - 2 - 1 14. ƒ1x2 = Œx + 1œ 15. ƒ1x2 = b 3 2 - 1 2 x if x 6 -2 if x Ú -2 16. The graph of y = ƒ1x2 is shown here. Sketch the graph of each of the following. Use ordered pairs to indicate three points on the graph. (a) y = ƒ1x2 + 2 (b) y = ƒ1x + 22 (c) y = -ƒ1x2 (d) y = ƒ1-x2 (e) y = 2ƒ1x2 17. Describe how the graph of ƒ1x2 = -22x + 2 - 3 can be obtained from the graph of y = 2x. 18. Determine whether the graph of 3x2 - 2y2 = 3 is symmetric with respect to the (a) x-axis (b) y-axis (c) origin. 19. Let ƒ1x2 = 2x2 - 3x + 2 and g1x2 = -2x + 1. Find each of the following. Simplify the expressions when possible. (a) 1ƒ - g21x2 (b) a f gb1x2 (c) domain of f g (d) ƒ1x + h2 - ƒ1x2 h 1h≠02 (e) 1ƒ + g2112 (f) 1ƒg2122 (g) 1ƒ∘ g2102 Let ƒ1x2 = 2x + 1 and g1x2 = 2x - 7. Find each of the following. 20. 1ƒ∘ g21x2 and its domain 21. 1g∘ ƒ21x2 and its domain 22. (Modeling) Cost, Revenue, and Profit Analysis Dotty starts up a small business manufacturing bobble-head figures of famous soccer players. Her initial cost is $3300. Each figure costs $4.50 to manufacture. (a) Write a cost function C, where x represents the number of figures manufactured. (b) Find the revenue function R if each figure in part (a) sells for $10.50. (c) Give the profit function P. (d) How many figures must be produced and sold for Dotty to earn a profit? x y (2, –1) (0, 1) 0 1 3 x y (1, –3) (0, 0) (4, 0) y = f(x)
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