Mount Olive High School Summer Assignment for

Transcription

1 Name: Mount Olive High School Summer Assignment for Precalculus CP Students who may wish to complete this packet: Anyone entering: Precalculus CP in September 2017 Directions: Skills Review It is necessary that you retain the skills you have learned in your previous math courses in order to be successful in precalculus. These skills are going to be built upon and not retaught in precalculus. Without these skills you will not be able to solve problems in precalculus. It will be assumed that you have these skills and they will not be retaught by your teacher. The answers to these skills test review problems are given in the back of this packet so you can check your work and make sure you understand the concepts. If you find that you have forgotten how to solve certain problems, you may need to go back through your notes and refresh your memory. We look forward to seeing you in September. Have a great summer!

2 Precalculus CP Summer Assignment 2017 Skills Review 1. What is a function? 2. Give a real world example of a function and draw a graph of it. 3. Which of the following relations is not a function? Why? a. b. x x y y c. d. x x y y If f (x) 20x 2x 2 then f ( 2) = 5. If f(x) = x 3 + x 4 and g(x) = 2x Evaluate (f + g)( 2) 6. Given m(c) c Given k(p) 20 p 2 Find m(2) 8. If f(x) = 18x 54 and g(x) = 2x + 1 Find (f g)( 1) Find k( 4) 9. If Tom takes 3 credits at CCM, it will cost him $900. If Tom takes 6 credits, it will cost $1500. Determine a linear model for the cost per credit. Find (fg)(x) 10. What is the slope in problem 9? What does the slope mean? 11. Given f (x) 2x 2 10x 1 find f (x 5) What is the y intercept of problem 9? What does it mean?

3 The graph below shows the number of people who will buy a product at each given price. Answer questions (a) (h) using the graph below. 120 [Number of people as a function of price. P($)] number of people price of product 20 a. How many people will buy the product when the price is $10? b. If you want 60 people to buy the product, how much should you charge for it? c. Find Domain of this function? d. Find Range of this function? e. Find P(8) f. Find P(16) P(4) and give practical interpretation (real world meaning) for your answer. 13. The function W(t) gives the gray wolf population in the United States. Where t number of years after What is practical interpretation (real world meaning) for a. W(40) 1700 b. W 1 (800) 0

4 14. Assuming the entire graph of function f(t) is shown, what is the domain of the function? a) [120,50] b) [0,24] c) (120, 50] d) (0, 24] 15. Answer questions (a) (c) using the graph below a. Find Domain. b. Find range. c. Write an equation for this piecewise function.

5 16. A person who is standing on the roof of a 200 feet tall building throws a ball. This ball flies downward and eventually strikes the ground. The function S(t) describes the ball s height above the ground in feet, t seconds after it was thrown. a. Interpret (give real world meaning) S(5) 4 b. Interpret (give real world meaning) S(k) 16 c. Interpret (give real world meaning) S(m) 80 d. Interpret (give real world meaning) S 1 (30) = 4 e. Give possible and reasonable domain for S(t) f. Give possible and reasonable range for S(t) 17. Five Longest-Running National Network TV Series of 20 th Century. Program Number of Seasons the Show Ran Walt Disney Minutes 33 The Ed Sullivan Show 24 Gunsmoke 20 The Red Skelton Show 20 a. Is Number of Seasons the Shows Run a function of program? WHY? b. Is Program a function of Number of Seasons Shows Run? WHY? 18. A person with a body weight of 100 pounds burns 2.7 calories per minute when walking at a rate of 3 miles per hour. A person with a body weight of 120pounds burns 3.2 calories per minute when walking at a rate of 3 miles per hour. Determine a linear model of how many calories a person of any weight burns if they are walking at a rate of 3 mph. If the calorie rate continues in a linear fashion, how many calories should a person burn who weighs 150 pounds?

6 19. The Population of a country with an initial population of 2 million people grows at a rate of 4 % per year. We can represent this function with the equation P(t) = 2(1.04) t. Let N(t) represent the number of people in millions that a country can feed in the year t. We want to express the surplus of food for the country in a year t as S(t). Which of the following would represent the surplus, S(t)? a. (N + P)(t) b. (N P)(t) c. (NP)(t) d. (N/P)(t) 20. If f(x) is an increasing function, what can you say about f( 2) and f(5)? 21. Given that g(x) = 3x + 4 find g 1 (x). a. f( 2) < f(5) b. f( 2) > f(5) c. f( 2) = f(5) d. It cannot be determined. 22. Given that f(x) = x find f 1 (x) 23. Find the zeros(x intercepts) of the following functions: a. f(x) = 3x 2 7x 6 b. g(x) = 3x What is the domain of f(x) = x + 5? Use interval notation. 25. f(x) = $1.35x + $2.95 represents the amount of cab fare you will pay when traveling on vacation where x is the number of miles you go and $ 2.95 is the cost of taking a cab. a. Evaluate f( 3) and state what it means. 26. Assume that gallons are a function of size and that G=f(s) is the amount of paint in gallons for a house of size s square feet. What is the practical application of f ( 750)? b. Find f 1 (x). Use f 1 (x) to evaluate f 1 ($8.35) and state what it represents.

7 27. Given the graphs of f and g below, evaluate g(2) f ( 1). f(x) g(x) 28. What is the equation of the piecewise function shown at the right? 7 30 x + ; 10 x < a) f(x) = { 2 ; 2 x < 2 x 2; 2 < x 10 b) f(x) = { x + ; 10 x < ; 2 x < 2 x ; 2 x 10 c) f(x) = { x + ; 10 x < ; 2 x < 4 x ; 4 x 10 d) None of the above

8 29. Use the graph shown below to answer the following questions. a) State if the graph is a function. If it is a function, give its domain and range. If it is not a function, state why it is not a function. b) A portion of this graph (not the whole graph) could represent the amount of money in a savings account that compounds interest monthly where x is the time in months and f(x) is the amount of money in the account in hundreds of dollars (100 s of $). Evaluate f (4) and state what it represents in this problem.

9 Skills Review Answers: 1. A function is a relation between two variables such that for every input there is only output. 2. Examples may vary. The graph must pass the vertical line test to be a function. 3. C, because when the input is 3 there is more than one output ; 36x 2 90x y = 200x The slope is 200. The slope is the cost in dollars for one credit at CCM. The y-intercept is 300. This represents a fixed cost you must pay regardless of how many credits you take, usually known as student fees x x 12. A. about 32 ; B. about $4.25 ; C. [ 0, 23 ] ; D. [ 0, 86 ] ; E. 40 ; F. 41 which is how many fewer people will buy the product if you raise the price from $4 to $ A. In the year 2000 the wolf population is 1700 ; B. When the wolf population is 800, the year is B 3 x x < 3 2 7x 18 3 x < 2 5x x < A. [ 5, 5 ] ; B. [ 4, 6 ] ; C. y = 5x x < 2 7x 18 2 x < 3 { 3 x x A. 5 seconds after the ball is thrown the height of the ball is 4 feet ; B. k seconds after the ball is thrown the height of the ball is 16 feet ; C. m seconds after the ball is thrown the height of the ball is 80 feet ; D. When the height of the ball is 30 feet the time is four seconds after the ball was thrown. ; E. [ 0, 6 ] ; F. [ 0, 200 ] 17. A. Yes. For every input (the TV program) there is only one output (the number of seasons) ; B. No. For every input (the number of seasons) there could be more than one output (the TV program). 18. m = = calories / pound so y = 0.025x where y is calories and x is pounds ; a 150 lb. person would burn 3.95 calories. 19. B 20. A 21. x x x = 2 3 and 3 ; x = [ 5, ) 25. A. (3) = $7.00, the amount you would pay to take a cab 3 miles. B. f 1 (x) = x 2.95 f 1 (8.35) = 4 which means if the cost was $8.35 then you traveled 4 miles. 26. The number of gallons you would need to paint a 750 square foot house ;

10 28. B 29. A. yes, a function. The domain is (, ) and the range is ( 0, ). B. f(4) is about 3.5. This means that after 4 months there is about $350 in the account.