Practice Test Chapter 6 Polynomial Functions

Transcription

1 FOM 12 Practice Test Chapter 6 Polnomial Functions Multiple Choice Identif the choice that best completes the statement or answers the question. Name: Block: _ 1. Determine the degree of this polnomial function: 5 A. 0 B. 1 C. 2 D x Determine the degree of this polnomial function: f(x) = + 2x A. 0 B. 1 C. 2 D Determine the equation of this polnomial function: 5 4 A. f(x) = x 2 3x 1 B. g(x) = x 2 2x + 1 C. h(x) = x 3 2x D. j(x) = x 3 + 2x x

2 4. The distance a marathon runner covers can be modelled b the function d(t) = 153.8t + 86 where d represents the distance in metres and t represents the time in minutes. Approximatel how long will it take her to run the 42.2 km race? A. 4.6 h B. 5.0 h C. 5.5 h D. 6.0 h 5. Use a ruler to help ou estimate the slope for a line that best approximates the data in the scatter plot. A. 1 B. 1 C. 2 D x 6. Describe the characteristics of the trend in the data A. increasing B. decreasing C. constant D. no trend x

3 7. Describe the characteristics of the trend in the data. x A. increasing B. decreasing C. constant D. no trend 8. What kind of relationship might there be between the independent and dependent variables in this scatter plot? A. linear B. quadratic C. cubic D. none of the above x 9. The path of a shot put thrown at a track and field meet is modelled b the quadratic function h(d) = 0.048(d d 26.28) where h is the height in metres and d is the horizontal distance in metres. What is the horizontal distance when the shot put is at its maximum height? A. 6.4 m B m C m D m

4 10. Determine the equation of the quadratic regression function for the data. x A. = 0.4x 2 0.6x B. = 0.4x 2 0.6x C. = 0.6x 2 0.4x D. = 0.6x 2 0.4x Short Answer 11. Determine the degree of this polnomial function: x Determine the degree of this polnomial function: f(x) = 10x 3 (5x 2x 2 + 3) 13. How man turning points does a degree 1 polnomial function have?

5 14. Describe the end behaviour of this polnomial function: f(x) = 5x 2 + x The distance a marathon runner covers can be modelled b the function d(t) = 153.8t + 86 where d represents the distance in metres and t represents the time in minutes. How far has she run after 90 min, to the nearest kilometre? 16. Determine the independent and dependent variables for the following relationship: The number of das is related to the height of a pea plant.

6 17. Determine the equation of the linear regression function for the data. Round all values to the nearest hundredth. x The tide depth in a Pacific harbour from noon on March 1, 2012 to noon the next da can be modelled b the cubic function f(t) = 0.001t t t where f is the tide depth in metres and t is the number of hours after noon. Determine the maximum tide depth during these 24 hours, to the nearest metre. 19. Determine the equation of the quadratic regression function for the data. Round all values to the nearest hundredth. x

7 Problem 20. Determine the following characteristics of the polnomial function f(x) = 5(x 1)(x 2 + 4). number of possible x-intercepts -intercept end behaviour domain range number of possible turning points 21. Write an equation for a polnomial function that satisfies each set of characteristics. a) degree 2, decreasing function, -intercept of 7 b) two turning points, ending in Quadrant I, -intercept of 4

8 22. A large biccle retailer collects data on the number of biccles in each store compared to floor space of each store. The data is given in the table below. Number of Biccles Floor Space (sq ft) a) Determine the equation of the linear regression function (round to the nearest tenth). b) What do the slope and -intercept represent in this context? c) Estimate the number of biccles in a store with 2500 sq ft of floor space. 23. Meghan screen prints T-shirts for sale at concerts. When buing blank T-shirts, the price Meghan must pa is related to the size of the order. Four of her previous orders are listed in the table below. Number of Shirts Cost per Shirt ($) Meghan has misplaced the information from her supplier about prices on bulk orders. She would like to get the price per shirt below $12.50 on her next order. Extrapolate the number of T-shirts she should order. Show our work.

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10 24. The first 30 m of the path of a roller coaster can be modelled b the regression equation = 0.008x x x where represent the vertical distance in metres and x represents the horizontal distance in metres. a) Use our knowledge of polnomial functions to describe the curve of this function. b) Compare the heights of the points at x = 0, x = 10, x = 20, and x = 30. What can ou tell about the shape of the curve from these values?

11 25. A college kept track of the attendance at varsit football home games in the table below. Game Attendance a) Use a scatter plot to determine the tpe of relationship (Linear, Quadratic, or Cubic). Then determine the regression function for this data. (Round to the nearest tenth) b) Use our curve of best fit to interpolate the attendance at the fifth game. c) Use our curve of best fit to extrapolate which game would have an attendance of about 3764