For questions 4-5, find the vertex, describe the transformation and draw a graph for each function. (2.1)

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1 PreCalculus Unit 3 Review Name: No Calculator Allowed 1. Write the equation of the line that passes through (3,10) and is parallel to 5 6y 33. (P.4). Write the equation of the line in general form through ( 3, ) that is perpendicular to 4 y 8. (P.4) 3. Find the equation of a line where f ( ) 5 and f (1) 7. (.1) For questions 4-5, find the verte, describe the transformation and draw a graph for each function. (.1) 4. 1 f ( ) ( ) 3 5. y f ( ) 4 3 y For questions 6-9, if the function is a power function list the constant of variation and the power. Then, sketch a graph for each function. If the function is not a power function, eplain why not. (.) 6. f ( ) 4 1/3 7. f ( ) 5 8. f ( ) f ( ) 1/ 4 Write the statement as a power function equation. Use k as the constant of variation. (.) 10. The area of an equilateral triangle varies directly as the square of the side s. 11. Out of all the cones with a fied volume, the height h of the cone varies inversely as the square of its radius r.

2 c 1. Find the logistic function of the form f( ) whose limit to growth is 60, initial value is 1, and passes through (1, 4). 1 ab (3.) Calculator Allowed 13. If the length of a rectangle is 3 meters less than four times the width, then write an equation for the area of the rectangle as a function of the width of the rectangle. (1.6) 14. Joe Pearlman received a 3.5% pay raise. His salary after the raise was $37,60. What was his salary before the raise? (1.6) 15. Sue invested $10,000, part at 3.6% annual interest and the balance at 7.8% annual interest. How much money is invested at each rate she received a 1-year interest payment of $ (1.6) For questions 16 and 17, write an equation and solve the problem. (-) 16. The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 3.5 sec when the length is 49 inches, find k, the constant of variation. Determine what the period is when L = inches. 17. The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is.5 lb when the masses are 4 ft apart. Find k, the constant of variation, and determine what the attraction is when the masses are 6 ft apart.

3 18. Larry uses a slingshot to launch a rock straight up from a point 6 ft above level ground with an initial velocity of 170 ft/sec. Use the fact that 1 h() t gt v t h 0 0. (-1) a) Find an equation that models the height of the rock t seconds after it is launched. b) What is the maimum height of the rock? When will it reach that height? Determine the answer algebraically and graphically. c) When will the rock hit the ground? Determine the answer algebraically and graphically. 19. Sarah s salary as an account eecutive is growing at a rate of 5% per year. Solve algebraically and graphically. (3-) a) If her initial salary is $36,000, how long will it take her salary to double? b) Write the doubling time equation for this situation. 0. On April 6 th 1986, one of the worst nuclear power plant disasters in history occurred when reactor number four of the Chernobyl power plant (Russia) eploded. The eplosion and resulting fire sent a plume of highly radioactive fallout into the atmosphere, blanketing the immediate area and also traveling across parts of the Soviet Union and into Europe. To this day, the radioactive levels surrounding Chernobyl are so high no human can live there. (3-) Among the different types of radioactive isotopes released from the eplosion was Pu-39. Pu-39 has a half-life of 4,400 years. The disaster released approimately 0 tons of Pu-39 into the area immediately around Chernobyl. a) Write a half-life equation for this situation. b) How much of the original 0 tons of Pu-39 remained 10 years after the disaster? 100 years after the disaster? 1. Use the TVM Solver: Find the payment made on the last day of each month for a 5 year $15000 car loan at 5.% interest. (3-)

4 . Given the data below from a college with an outbreak of a contagious flu virus. (3.5) Number of Students Day with flu a) Determine which model (linear, eponential, logistic or logarithmic) best represents this data and find an equation for number of people with the flu as a function of the number of days after the outbreak began. b) How many students, to the nearest whole student, attend this college? c) The college will cancel classes when 40% of the students have the virus. Assuming nothing is done to deter the spread of this flu, on which day after the outbreak will the college cancel classes? Solve graphically. 3. The table shows some data for a chess player s rating given the number of years the player has studied chess (for one hour a day). (3.5) a) Determine which model (linear, eponential, logistic or logarithmic) best matches this data. Eplain. Years Studying Chess Rating b) If Mr. Madsen has been studying chess for.5 years, what can he epect his player rating to be? c) A Grand Master player has a rating of 500. According to your model, how many years would it take a player to become a Grand Master? What could you do to get to this rating faster? 4. Using 0th century US census data, the populations of New York state can be modeled by Pt () t 1 61.e where P is the population in millions and t is the number of years since (3. and 3.5) a) What was the population of New York in 1800? b) About when will the population of New York be 19 million people according to the model? Solve algebraically.

5 I 5. The relationship between intensity I of light (in lumens) at a depth of feet in Lake Erie is given by log What is the intensity at a depth of 5 feet? Solve algebraically and graphically. (3. and 3.5) 6. A mass on a spring oscillates back and forth and completes one cycle in 0.8 seconds. Its maimum displacement is 7 cm. Write an equation that models this motion. (Assume the mass begins in the middle). (4.8) 7. Ally is at summer camp swinging on a rope tied to a branch going back and forth alternately over land and water. Nathan starts a stopwatch. When = seconds, Ally is the furthest from the riverbank over land (as shown in the picture) at y = 3 feet. When = 5 seconds, she is the furthest from the riverbank over water at y = 17 feet from the river bank. While she is swinging a sinusoid equation models the distance from the river bank s edge as a function of the time she is swinging. (4.8) a) Sketch a graph to model the distance from the river bank s edge versus time. b) Determine the sinusoidal equation to model the distance from the river bank s edge as a function of time. c) What is Ally s distance from the river bank after 13. seconds? Was she over land or water at this time? Eplain. d) Determine the first positive time when Ally was directly over the river bank. REMEMBER any problems from quizzes or HW worksheets are fair game for this test.