f x 3x 5x g x 2x 4x Name Date Class 2 nd Six Weeks Review 2016 PreAP PreCalculus Graphing calculators allowed on this portion. 1.
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1 Name Date Class nd Si Weeks Review 016 PreAP PreCalculus Graphing calculators allowed on this portion. 1. Find all roots of f 5 7 by using the quadratic formula.. Find all roots of g 4 1 by completing the square. Perform the operation and write the result in standard form.. 5i i i 6. i 5 10
2 For the given interval: (a) State the domain for the function on the interval. (b) Does the Intermediate Value Theorem guarantee that f(c) = a? (c) Justify your answer. 7. f 9 f 1 c [ 5,5] 8. g 9 g c 0 [,] 9. h h c [4,9] 9 Find the function y = f() that satisfies the equation with the given initial conditions. 10. y e C f ln y C f y e C f 0 1. y C f 8
3 14. A population of animals is modeled by the function P t 0. measured in years. The year 015 is t=0. (a) Determine the carrying capacity of the environment. 400 t 1 4e, where t is (b) What was the population in 015? (c) What is the predicated population for the year 00? (d) When is the population predicted to be 00? 15. The rate at which a rumor spreads through a high school can be modeled by the function 000 R t 0.6t 1 500e, where R is the number of students who have heard the rumor t hours after 9AM. (a) What s the total number of students in the high school? (b) How many students have heard the rumor by noon? (c) At about what time will 900 students have heard the rumor? (d) About how many students have heard the rumor by 9PM?
4 16. Assume that a colony of bacteria grows according to the law of eponential change. If the number of bacteria doubles in 5 hours, how long will it take for the number of bacteria to triple? 17. The skull of an animal found in an archaeological dig contains about 0% of the original amount of carbon-14. If the half-life of carbon-14 is 570 years, how long ago did the animal die? 18. A substance decomposes according to the law of eponential change. If the amount was 40g after 1 hour and 10g after hours, then how much of the substance was originally present? At what time will only 1g remain? 19. The concentration of a medication injected into the bloodstream drops at an eponential rate. If a 100 mg dose reduces to 80 mg in about 1 hour, how long does it take for 90% of the medication to be absorbed?
5 Solve for. Round answers to the nearest thousandths e ln ln 1. log e 6. log log 7. log 9 11 log9 0
6 This portion of the review is to be completed without the aid of a graphing calculator. For each eponential function, name the horizontal asymptote, range and y-intercept. Then, make a table of values for the eponential function by transforming the parent function, and sketch a graph using at least three points. Describe the rate at which the function is increasing or decreasing f 9. g 1 4
7 For each logarithmic function, find the domain, -intercept and vertical asymptote, make a table of values for the logarithmic function by transforming the parent function, then sketch a graph using at least three points. Describe the rate at which the function is increasing or decreasing. f log g log 4 1.
8 Find the zeros of each function, make a sign chart (behavior line), and then sketch its graph.. y y y 1 4 y
9 6. y y For each rational function, (a) find all intercepts, (b) find all asymptotes, and (c) use the given information to sketch a graph of the function. 8. f Concave up for <, Dec for < < 8., Inc for > 8. Points (8., -1.5)
10 9. g Concave down for < -1, Concave up for > -1 Points (-, -.5) and (1, 4.5) Solve each inequality and write your solution in interval notation
11
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