Functions Review (Quadratic, Exponential, Step and Periodic)
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1 1. If you have a quadratic function and one of the points is (27, -9). What is the rule of the function. 2. John and Jim are going for a ride in a hot air balloon. A monitor inside the basket records how high they have travelled according to the time that has passed in minutes. The function f(x) represents their climb into the sky: f(x) = 1.25x 2 where f(x) represents their height in meters x represents the number of minutes that have passed. In how many minutes will they be at a height of 61.25m? 3. A store owner sells square ceramic tiles of different sizes. The function described below can be used to determine the cost of a tile according to the length of one of its sides. f(x) = x 2 where x: length of a side of a tile, in centimetres f(x): cost of a tile, in dollars Lawrence bought tiles that cost $1.17 each. What is the length of a side of the tiles that Lawrence bought? 4. Jonathan has built a go-kart. Today, he tested his go-kart on a hill. As the cart went down the hill, it kept picking up speed. Some of Jonathan's friends took measurements at different times. The following table of values shows the measurements they recorded. After it set off down the hill, how long did it take for the go-kart to travel 20m? Time (s) Distance (m)
2 5. If you know population of St. Bruno that is increasing at a rate of 2.5% and there are people. What will the population be in 4 years? 6. Upon exposure to the sun, a 10-kg block of ice loses 30% of its mass for each minute that elapses. What is the mass of the block of ice after 300 seconds of being exposed to the sun? 7. Stephan is trying to save $2000. Stephan's plan is to put $1000 into a savings account that will earn 8% per year. How long will it take for him to save the desired amount? 8. On the same day in January 2010, Daniel bought a truck and Jack bought a car. Since then the value of each vehicle has decreased annually with respect to its previous year's value. The following function describes how the value of Daniel's truck has decreased f(x) = 31000(0.89) x where x = years since purchase f(x) = value of truck Jack paid $25000 for his car in January 2010 and his car has been depreciating at rate of 12% annually. When Daniel's truck is worth $ , how much will Jack's car be worth? 9. Macrohard Software and Computers Inc. has been manufacturing processors since They estimate that the speed of their top processor has increased by 15% every year. On January 1, 1982, the speed of their top processor was 60 MHz. This situation is represented by the rule given below: F(x) = 60(1.15) x where x = # of years since January 1, 1982 F(x) = Speed of the top processor What will the speed of the company's top processor be on January 1, 2012?
3 10. The graph below shows that different age groups pay different ticket prices to attend a junior hockey game. Which of the following statements is true? a) A 15-year old pays $4 and a 16-year old pays $8 b) A 5-year old pays $2 and a 15-year old pays $8 c) A 5-year old and a 65-year old both pays $4 d) A 5-year old pays $2 and a 65-year old pays $ The maximum speed allowed on a certain street is 50 km/h. Those motorists caught exceeding these speed limits are fined by the police. Fine ($) Speeding Fines Excess speed (km/h) Which of the following statements is TRUE? A) A motorist driving at 50 km/h will be fined $50. B) A motorist driving at 30 km/h will be fined $100. C) A motorist driving at 40 km/h will be fined $225. D) A motorist driving at 10 km/h will be fined $300.
4 12. Given the following step function determine which of the statements below are false. a) The first hour of parking is free. b) It costs $4 to park for 3 hours. c) It costs $8 to park for 4 hours. d) The maximum cost to park is $ The function represented below can be used to determine the cost of printing a yearbook according to the number of pages it contains. The graduates of a secondary school want to print 30 yearbooks containing 20 pages each for teachers and 100 yearbooks containing 36 pages each for students. How much will it cost to print all 130 of these yearbooks? 14. If the Period for h(t) is 8. Find a) h(-5) b) h(31)
5 15. The periodic function represented below can be used to determine the distance between the train and the station in relation to the time elapsed from the moment the train sets off. Exactly 165 minutes after the train sets off, how far is it from the station? A) 0 km B) 1.25 km C) 1.5 km D) 2.25 km 16. The ECG tracings below represent the heart beat of a patient. Assume that the heart beat remains stable over the next few minutes. Calculate the voltage of this patient s heart rate at 4.57 seconds.
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