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Study Guide For Honors Pre-calculus Final Date: December 16,2013 Chapters 1-6 except 5.4 Read Chapter Summaries at the end of each chapter. Study the chapter tests. Solve the following review problems: 1. State the domain of the following function in interval notation: f ( x) [A] 7, [B] 7, [C] , 5 x7 [D] , 7 7, 2. Which of the following must be true? I. If f(x) = x3/4 – 1 and f(k) = 63, then k = 64. II. If ( 8x)(1/2)x-1 = 163x, then x = 1/10. III. If 5x+5x+5x+5x+5x = 525, then x = 5. IV. A) B) C) D) E) If f(x) = , then g(x) = f-1(x) = . I and II II and IV III and IV I, II, and IV II, III and IV 3. Solve the quadratic inequality for x: [A] , 3 or 5, [B] 3, 5 x 2 2 x 15 0 [C] , 3 or 5, , 4 or 2, 5 [C] , 4 or 2, 5 2 [D] , 4 or 2, 5 5. State the domain of the following function: 3 , 4 [A] 3, 5 x5 0 x 2x 8 [B] 4, 2 or 5, 4. Solve the rational inequality for x: [A] [D] 3 [B] , 4 y 3x 4 4 , 3 [C] 4 [D] , 3 6. If f ( x) f ( x) for every value of x in the domain of the function f , then which one of the following is true about f ? [A] f is called an odd function and its graph is symmetric about the y-axis. [B] f is called an even function and its graph is symmetric about the y-axis. [C] f is called an odd function and its graph is symmetric about the origin. [D] f is called an even function and its graph is symmetric about the origin. 7. The graph of y 3 x 5 can be obtained by doing which of the following transformations of the graph of y x ? [A] reflect about the x-axis, stretch by a factor of 3, shift up 5 units. [B] shift down 5 units, reflect about the y-axis, stretch by a factor of 3. [C] reflect about the x-axis, stretch by a factor of 3, shift down 5 units. [D] reflect about the x-axis, shrink by a factor of 3, shift down 5 units. f 5 g 8. If f ( x) x 2 9 and g ( x) x 3 , then [B] x 3 [A] 5( x 3) 9. If f ( x) 2 x 4 and g ( x) 3x 1 , then [A] x 3 [C] 1 8 [D] 8 f g ( x) [C] x 3 [B] 5 x 2 3x [D] 5x 3 10. If f ( x) x 2 1 and g ( x) x 2 , then ( f g )( x) [A] x 2 4 x 5 [B] x 2 3 [C] x 2 1 11. If f ( x) 7 x 3 and g ( x) x 2 4 , what is ( f g )( 2) ? [A] 53 [B] 59 [C] 125 12. If f ( x) [A] 4 3x 8 3 x 2 , then f 1 ( x) 4 4 8 [B] x 3 3 [C] 4 8 x 3 3 [D] x 2 2 x 5 [D] 292 [D] 4 x2 3 13. Which one of the following is true about the graph of a one-to-one function of x ? [A] It is symmetric about the y-axis. [B] It is symmetric about the x-axis. [C] It will pass through the ordered pair (1, 1). [D] It will pass the horizontal line test. 14. Which one of the following equations have the given roots, 3 and 4i ? [A] x 3 3x 2 16 x 48 [B] x 3 3x 2 16 x 48 [C] x 3 3x 2 16 x 48 [D] x 3 3x 2 16 x 48 15. Write the following as a product of linear factors given that 1 and 3 are zeros: f ( x) x 4 2 x3 x 2 8x 12 [A] ( x 1)( x 3)( x 2i )( x 2i ) [B] ( x 1)( x 3)( x 2i )( x 2i ) [C] ( x 1)( x 3)( x 2i )( x 2i ) [D] ( x 2)( x 2)( x 3)( x 1) x2 4 x2 [B] , 2 or 2, 16. State the domain of the following function in interval notation: f ( x) [A] , 2 or 2, [C] , 9 7 [B] y 0 [A] x 1 , x5 2 [B] x 1 , x 5 2 4 7 2 [D] y 0 5x 2 4 x3 4 [C] ,0 3 [B] 0, 4 3 f ( x) [B] (5, 0) [D] (3, 0) 5 x x5 [C] (1, 0) 21. If P varies inversely as w, and P [A] 1 [D] y f ( x) 20. Find the x intercept: [A] (0, 1) 1 4 4x 9 2x 9x 5 9 [C] x 4 f ( x) 19. Find the y intercept: [A] (0, 3) x [C] 18. Find the vertical asymptote(s): 2 or 2, 2 or 2, 4x 1 7x 9 f ( x) 17. Find the horizontal asymptote: [A] y , [D] [B] 16 [D] (–1, 0) 2 1 1 when w , then what is P when w ? 3 4 6 4 [C] [D] 4 9 22. If y varies directly as u and varies inversely as the square of v, and y 7 when u 9 and v 6 , then find the constant of variation. [A] 7 6 9 [B] 7 4 [C] 28 9 [D] 28 23. The number of spiders, S (t ) , remaining within a 10-foot radius of their birthplace t days after birth is given by the formula: S (t ) 200 20.2t . Find the number of spiders present within this radius 10 days after their birth. [A] 0 [B] 5 [C] 50 [D] 800 A) B) C) D) E) 24. What are the zeros of the equation 4x-1-20x-2-24x-3 = 0? 0, 6,-1 0,2, -3 0, -6,1 6,-1 -1,6 8 2 1 [C] log3 (2) 8 [D] log 8 2 3 3 25. Write the equation in its equivalent logarithmic form: [A] log 2 (8) 3 [B] log 8 (2) 1 3 1 729 26. Evaluate the expression: log 9 [A] 3 [B] 3 27. What is the domain for f ( x) log 2 ( x 1) ? [A] 0, [D] 81 [C] 81 [B] 1, [C] 1, [B] log b (8) log b (8) log b (3) log b (3) [D] (, ) 28. Which one of the following is true? [A] e ln(x ) x for any real number x. [C] log b (8) 8 log b (3) 3 [D] log 2 (7) 29. Write as a single logarithm whose coefficient is 1: [A] logb (13) log( 7) log( 2) 2logb (8) logb (3) 64 3 [C] log b [B] logb (61) 30. Expand the logarithmic expression: ln 3e 2 [A] 2 ln(3) ln(e) [B] (2 ln 3) 1 [C] 2 ln(3) [D] logb (10) [D] 2 ln(3) 31. If 5 x 29 , then x equals [A] ln(29) ln(5) [B] ln(5) ln(29) 29 5 [C] ln 5 2 [D] ln 32. Solve for x: log 7 (3x 9) log 7 (2 x 6) 0 [A] 3 [B] all real numbers [C] 3 [D] No solution 33. Solve for x. If there are two solutions, state their sum. If there is one solution, state that answer. log( x 9) log( x ) 1 [A] 9 [B] 9 [C] 1 [D] 1 34. If $2500 is invested in the account that pays interest compounded continuously at a rate of 4%, how long will it take to double the investment? Hint: A Pe rt [A] 2.8 years [B] 13.0 years [C] 14.2 years [D] 17.3 years 35. The spread of a flu virus through a particular population is modeled by y 1000 where y is the total 1 990e0.7 t number of people infected after t days. In how many days will 530 people be infected with the virus? (Round your answer to the nearest whole number.) [A] 8 days [B] 9 days [C] 10 days [D] 11 days 36. Which of the following functions has a zero, vertical asymptote and a horizontal asymptote? A) B) C) 37. Describe the transformation from f(x) to g(x): f(x) = ex and g(x) = e5x- 5 f(x) is: A) Compressed horizontally by a factor of 5 and shifted down by 5 units. B) Stretched horizontally by a factor of 1/5 and shifted down by 5 units. C) Compressed horizontally by a factor of 1/5 and shifted right by 5 units. D) Stretched horizontally by a factor of 1/5 and left by 5 units. E) Compressed horizontally by a factor of 1/5 and shifted down by 5 units. D) 38. Which of the following is false about f(x) shown above? A) It is an even function. B) It s degree is 3. C) It has 2 absolute minima and 1 relative maximum. D) It is decreasing for all real numbers o x less than -1 and between 0 and 1. 39. Which of the following can be the equation of the graph above? A) (x+2)(x-2)² B) (x-2)³ C) (x+2)²(x-2) D) (x-2)²(x+2)²