Pre-AP Pre-Calculus - Summer Assignment

Transcription

1 Pre-AP Pre-Calculus - Summer Assignment PreAP Precalculus is a rigorous critical thinking course. Our expectation is that each student is fully prepared; therefore, the following Algebra II concepts must be mastered prior to the beginning of PreAP Precalculus. Simplifying complex fractions Simplifying rational expressions and working with rational and negative exponents Factoring Function operations, compositions, and inverses Solving equations Linear Quadratic Equations with rational exponents Basic log and exponential equations Rational equations Writing and graphing equations of lines Characteristics of graphs Intercepts Domain and range Max and min Writing equation from a graph Vertical and horizontal transformations of functions Parent functions If you struggle with any topics and want to review, one web site is by Paul Dawkins of Lamar University, Dr. Dawkins has many notes, sample problems and tutorials that you may find helpful as you review. Another good web site for review is where you will find a wealth of review material. In order to ensure that you complete the packet, we will be testing over this material sometime during the first week of school. The test will be part calculator, part non-calculator. You will have a chance to get your questions answered the first day or so of school. It will count as a homework grade. Remember, I am not available for tutoring during the summer. I look forward to meeting you in August! TCA contact: Mrs. Cyphert, cyphert@tcaeagles.org

2 Pre-AP Pre-Calculus Assignment Name: All problems should be worked on separate paper without the aid of a calculator unless otherwise specified. All work must be shown. I. Simplifying Complex Fractions. 6. z z z. x y x xy y a b a b. II. Simplifying Expressions 5. s t s t 6. x m- x x m a x 5x 6x 5x. a c a c a c 0.. a a a 5mm m 7m III. Factoring. (Don t forget to look for a GCF!). 5x x 5. x x 5x mn 0n m 5 8. h 7h k 5hk 9. x 8 IV. Solving Equations z z x 5x 0. x 9 5. x 8. log5 x 5. 5 x 5 6. x x x x x x 8. x x x 5 9. x 0. x 9x 5. x 5

3 V. Equations of Lines For, write the equation of the line described. State your answer in the form specified.. passes through the, point-slope form and is perpendicular to the line x y 7 ;. slope is undefined and passes through the point, 5. x-intercept is 5 and y-intercept is ; standard form 5. Two values of a linear function f x are f and f equation of f x. 5. Find the 6. For several mammals, the gestation period, in days, and the average life span, in years, is recorded below: Animal Gestation (days) Average Life Span (years) Rabbit 7 Dog 60. Squirrel 9 Wolf 6.6 a. Using your calculator s regression capabilities to find L(G), the linear function of best fit for this data. Write decimal values correct to three decimal places. b. Use L(G) to predict the average life span of a kangaroo with a gestational period of 5 days. Give your answers correct to three decimal places and include units of measure. c. What are the units of the L intercept? What is the meaning of the L intercept? Could this situation occur? d. What are the units of the slope? What is the meaning of the slope in the context of this problem? e. What is the meaning of (8, 8) in the context of this problem?

4 VI. Function Operations, Compositions, and Inverses For 7, use f x x, g x x, hx x 7. h a 8. h f x 9. g x hx 0. f g. f x h f x. h x. f ( x) g ( x ). g hx 5. Given f and the fact that g x f x 5 to find g. VII. Finding Domain State the domain of each function. 6. f x x 7. f x x x 8. f x x 6 9. f x log x VIII. Applications of Systems of Equations 50. A 0 m ladder and a 5 m ladder were leaned against a building. The bottom of the longer ladder was 7 m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find the distance. 5. Four squares, each with sides cm long, are cut from the corners of a rectangular piece of cardboard having area 560 sq cm. The flaps are then bent up to form an open-topped box having volume 960 cu cm. Find the dimensions of the original piece of cardboard. IX. Transformations of Functions Describe the sequence of transformations from the parent to the given function. 5. f x x 5. f x x 5. f x x

5 X. Characteristics of Graphs For each graph, estimate the x and y intercepts, state the domain, range, and any max or mins. 55. (-, ) 56. (, -.5) XI. Parent Functions For each parent function, give the equation, sketch the graph, and give the domain and range. List asymptotes where applicable. 57. constant 58. identity 59. quadratic 60. absolute value 6. square root 6. cubic 6. reciprocal (rational) 6. exponential 65. logarithmic XII. True-False 66. 9x 9x 67. x x x x x 5x x y y x 70. x y x y 7. x 9 x 7. x x x ln t s t e 7. s e e

6 PreAP Precalculus Summer Assignment Key.. z +. y x y x. ab 5. st m 6. x a a a x (x). x (x). a c a c m. m x 5 x 5 x. 5. non-real factors x x nm 5 8. hh k h 5k 9. x x x ,. 7, ,, 7. 8., , -., -. y x. x =.x +5y = 5 5. f x x L G G 6a b. L yrs. c. L-intercept is in years. It means that a mammal with a gestational period of 0 has a life span of.90 years. d. m = yrs/day. Average life span increases.9 years when gestational period is one day longer. e. A mammal with gestational period of 8 days is expected to live 8 years a 8. x 9. x x x h xh h h x x. 5. x x x. x 6x x 7. x 8. x 6 9. x 50. cm 5. 0 cm x 8 cm 5. vertical stretch by horiz. shift right vertical shift up 5. vertical reflection over x axis 5. horizontal shift left vertical shift down 55. x-int: 0.8,.,.9 y-int:.8 domain: range: relative max: when x = - relative min: -0.5 when x = 56. x-int: y-int: -0.7 domain:, range:, absolute min: - when x = F 67. T 68. F 69. F 70. F 7. F 7. T 7. T 7. F