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15. Graph the ellipse when k = 3. 16. For what values of k is this the equation of a circle? 17. Graph the following hyperbola and find its asymptotes: 4 2y = i 50 CHAPTER TEST 5B 1. Consider two line segments, one with endpoints (3, 5). 0, 3) and (-2, 8 ) . Find the midpoint of the line segment whose endpoints are the midpoints of the two given line segments. 2. Let AB be a line segment on which the coordinates of A are (0, 10). Let C be the midpoint of AB and let D be the midpoint of AC. If the coordinates of D are (1, 7 ) , find the coordinates of B.

6. Find the domain of g(x) . 7. Find the range of ^(a;). 8. Find I J- J (j:) . 9. Find the domain of = /x - 4. (i)< i)"> 10. Find {g ° f) (x). 11. Find /" 1 (x) . 12. / o f) (χ) . 13. Find (f ° f) "1 (x) . 14. Find (/_1 o/" 1 ) (J;) . 15. Find the equation of the line that passes through (2, 3). and is perpendicular to the line through (1, 2) and (3, 5 ) . 27 CHAPTER TEST 3D 16. If I determine where fix) x2 x < 0 x 0 < x < 1 1 X > 0 is increasing, decreasing, and constant. 17. The force of attraction between two bodies is inversely proportional to the square of the distance between them.

Log (x + 1) + — log (x - 1) ■i 2 2 log (x 2 4 2 2 - 5) - i log (1 - x) 2 + 2 2 39 CHAPTER TEST 4A In Problems 15-18 solve for x. 15. 16. 17. 18. log 16 = 4 ^x 4*-i log (Ax - 4) = 2 40 CHAPTER TEST 4B In Problems 1-3, if log 3 = x, log 4 = y, and log 5=2, evaluate the given logarithm in terms of Ä , y, and z. 1. log 48 2. 75 3. 4 In Problems 4-8 simplify. 4. l0g 5. log _ 49 6. log 4 7. log 7a V7 8 64 32 8. l o 9. 9128 ά How long will it take to triple the amount of an initial investment if the annual rate of return is 15 percent compounded continuously?