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Math 1304 Final Exam Review 1. Factor completely. a. (6 x 1) 3 (27 x 2 2) (9 x 3 2 x)(3)(6 x 1) 2 (6) (6 x 1) 6 1 1 b. ( x 2 4) 2 (3)( 2 x 1) 2 (2) (2 x 1) 3 (1 / 2)( x 2 4) 2 (2 x) 2. a. Rationalize the numerator. b. Rationalize the denominator. x 2 x 2 x 3 x 3 3. a. Write the equation of the perpendicular bisector of the segment whose endpoints are (3,-10) and (5,11). b. Write the equation of the line tangent to the circle with center (6,-1) at the point (-2,4). 4. Find the domain. Write in interval form. f ( x) x3 x5 5. Suppose f(x) is given. Describe the following transformations. a. b. c. d. e. y=f(x)+8 y=f(x-2)-2 y=f(-x) y=1/2f(x) y=-f(x+3) Suppose f ( x) x 1 and g ( x) x 2 3x . Find: 6. a. f g (x) 7. a. f 8. a. 1 b. g f (x) b. g 1 ( x) ( x) f ( x h) f ( x ) h b. g ( x h) g ( x ) h 9. Find the zeros and use sign analysis to graph. p ( x) 3 x 4 2 x 3 x 2 10. Find all asymptotes, holes, intercepts, and graph. y x3 x x 12 2 Solve the following equations. 11. a. 101 x 6 x b. e 32 x 4 12. a. 2 log x log 2 log( 3x 4) b. log 5 x log 5 ( x 1) log 5 20 13. a. ln( x 4) 3 b. log x log( x 3) 1 14. sec x 3 and x is in quadrant IV. Find all trig functions. 2 15. Find the amplitude, period, phase shift, vertical shift, and graph. y 3 cos 4( x 8 ) 16. Find exact values. a. cos 750 b. tan 5 2 17. Verify the identity. 2(tan x cot x) sin 2 x tan 2 x cot 2 x 18. Use the sum and difference formulas to find the exact values. a. cos 165 tan 73 tan 13 b. 1 tan 73 tan 13 19. Solve over 0,2 sin 2x cos x 0 20. The Great Pyramid of Egypt is 147 meters high, with a square base of sides 230 meters. Approximate the angle formed when an observer stands at the midpoint of one side and views the apex of the pyramid.