Summer Assignment for AP Calculus AB

Transcription

1 This assignment is a review of Pre-calculus and Algebraic concepts that you need to be familiar with in order to make a smooth transition into AP Calculus AB. It will be due when you return to school on August 6, 08 - NO EXCEPTIONS. I would suggest that you complete this during the last few weeks of summer so that it is fresh in your mind. A test over this material will be given on Thursday, August 9 th. I look forward to meeting you in class this fall and a great school year! I hope you have a great summer! - Coach Crawford For help on Precalculus concepts: Scroll down on the home page to see many topics of interest. I. Analyzing Functions Use the figure at the right to answer the problems below:. Use interval notation to determine the interval on which the function, f( ), is Increasing: Decreasing: Constant: Concave Up: Concave Down:. The zeros of the function are =. For what values of are f discontinuous? = 4. Find the following information about the given graph. Be careful when to use -values and y-values! a. Domain b. Range c. Intervals of increase d. Intervals of decrease e. Relative (local) maimum f. Relative (local) minimum g. Absolute maimum h. Absolute minimum i. -intercepts j. y-intercept k. Even, odd, or neither l. Ending behavior:

2 5. Let f = and 9 g =,, find the following. State domain restrictions when necessary. + f = a. f g( ) = b. g f ( ) = c. d. Domain, range and zeros of f( ) e. Domain, range and zeros of g Find f then verify that it is the inverse by doing ( f f ) = and ( ) for the compositions SHOULD NOT BE INDENTICAL! f f =. Your work 6. f = + 7. f = Graph the piece-wise function, then evaluate the function at the values indicated. +, > 8. f = + 4, 9. ( a) f = ( b) f = ( c) f 5 = f <, 4, = +, < >, ( a) f 5 = ( b) f = ( c) f = ( d) f 0 =

3 Determine which functions are odd, even or neither. Be able to eplain both graphically and algebraically. 0. f 7 =. f 4 =. f = f = + 4. f = + 5. f = sin + Find the domain of each function. Recall: The denominator of a rational function can never = 0 and any radical with an even inde can t have a negative radicand f = 7. g = h 5 6 = j = 0. k = + +. y = + 9 Asymptotes: State the equation for the vertical and horizontal asymptotes for the following functions. Find the coordinates of any holes the function has f =. g = 4. f = 9 8 II. Simplifying and Solving Equations and Inequalities Simplify the following:

4 8. e ( ) e ( ) y + y y Solve each of the following for. 0. 9= = = = 4. + sin = 5. ln = 0 6. ln = 7. ln = e = 0 Solve the following over the interval[ 0, π ). 9. cos = sin sin + = 4. sin = 0 4. sin cos = 0 4. cos 4 = sin + = Rewrite each of the following as indicated. 45. Write cos θ = sin θ in terms of sin θ. 46. Write cos θ cos θ = in terms of cos θ.

5 Solve inequality and graph the solution on the number line provided. 47. > > 50. < III.Evaluating trigonometric functions. Solve for the principal values only WITHOUT a calculator. 5. cos π = 54. sin π 6 = 55. sec 0 = 56. tan 90 = 57. ( ) csc 50 = 58. csc π 5 = 59. cos 0 = 60. cot π = 6. sin = 6. cos ( ) = 6. tan () = 64. arcsin ( ) = 65. arctan ( ) = 66. sec ( ) Solve for ALL solutions without using a calculator. 67. sin θ = θ = arc = 68. sin θ = θ =

6 IV. Logarithms and Eponentials Evaluate each logarithm or eponential WITHOUT using a calculator. 69. log 8 = 70. log 4 64 = 7. log0 log5 7 = 7. 5 = 7. ln e = 74. log = 75. ln = 76. log5 = = = = = 8. 7 = 8. = = 84. What is significant about the answers to 74 76? Eplain. Solve each equation ALGEBRAICALLY. 85. = = 86. ( ) log ln + 4 = 0 = = = = = V.Lines Find the equation of the line going through each set of points. Use the Point-Slope Formula: y y m( ) y y = Recall: m = 89. (, ),( 5,6 ) 90. (, ),( 5,0 ) 9. (, 7 ),(,4) 9. ( 5,5 ),( 8,5 ) Write the equation of a line that fits the required directions: 9. The equation of a line parallel to #8 going through (,). 94. The equation of a line perpendicular to #8 going through (,5). 95. The equation of a line parallel to #8 going through (,4). 96. The equation of a line perpendicular to #84 going through the point (-5,).

7 VI.PARENT FUNCTIONS 97. Graph each of the parent functions and be familiar with them enough to graph them later WITHOUT the use of a calculator. f. f = g. f = h. f = i. f( ) = + j. = k. f f 9 f = = l.

8 98. Use FIVE (5) points to graph each of the trig functions below. Graph ONE period starting at the y-ais. Label the aes. a. f = sin b. f = cos c. f = tan d. f = tan VII.FORMULAS and OTHER You should have the following trig identities MEMORIZED and be able to use them.

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