1. Fill in the tables below for each of the following polynomials: [K10] a) f(x)=x-13x+3x-9 Degree...

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1. Fill in the tables below for each of the following polynomials: [K10] a) f(x)=x²-13x²+3x-9 Degree Type of polynomial b) f(x)=6x4 +7x²-8x+9 Degree Type of polynomial Sign of leading End behaviours coefficient Sign of leading End behaviours coefficient Domain Domain 2. Fill in the table below for the polynomial function: [K9] f(x)=(x-4) (x+1)²(x-5) x-intercepts and behaviour of graph at each x - intercept y - intercept End behaviours 3. Solve the following equation algebraically. Explain your process. [A6], [C3] 0=18x4+87x³+3x²-108x 4. a) Describe the transformations on the cubic function below. Explain your thinking process. [C4] f(x)=7 [(x-5)]³¹-45 b) The point (-9, -2446) is on the transformed function f(x)=7 [Cx-5)]³-45 use the transformation statement the find the original point on the parent function. Justify your answer. [T3], [C2] 5. Determine the values of m and n for f(x)=mx³+20x²+nx-35 given that (x+ 1) gives a remainder of zero, and when divided by (x-2) the remainder is 45. [T5], [C3] 6. Use algebra to determine whether the following function is even, odd or neither. [A6] a) b) f(x)=55x4-x²-78 f(x)=37x¹+93x ctions There are 10 questions in this Assessment of Learning for a total of 60 marks. Show all work for each question. 1. Determine the average rate of change of y in the function y = 2x³ + 7x² + 2x - 3 over the interval [3,5]. (5 marks) 2. Given the function f(x) = 2x² + 3x + 1, a. Use the secant method to find the instantaneous rate of change whenx= 1. (4 marks) b. Use First Principles to find the value of the derivative when x = 1. (4 marks) c. What did you notice? (1 mark) 3. Explain the difference between a secant line and a tangent line. How do they relate to the rate of change of a function? Include a sketch of each type of line in your solution. (6 marks) 4. The path of a baseball relative to the ground can be modelled by the function dur) = -f² + 8 + 1, where dur) represents the height of the ball in metres, and represents time in seconds. a. Find the average rate of change of the ball between 1 and 3 seconds. (4 marks) b. Using the secant method, find the instantaneous rate of change at 2 seconds. (8 marks) 5. a. Evaluate lim (3x³ +7x-16). b. What is the meaning of this value? (2 marks) 6. Evaluate the following limits. x²-16 a. lim X-4 x-4 &r _5r+17 x6x²+2x²-4x b. lim. c. lim A-40 d. lim 3+2 (3 marks) 49+h-7 h y²-8 2y²-7y+12 4 e. lim 2+h A+0 h 2 (2 marks) (3 marks) (4 marks) (2 marks) (3 marks) 7. Find the slope of the tangent line at point (-2,2) on the curve fux) = 2x² + 3x using First Principles. (4 marks) 8. Find the derivative of the function f(x) Principles. (4 marks) = 2 x - 10x + 3 using First 9. Using first principles, determine the equation of the tangent line at point (2.2) on the curve f(x) = x ² = 7x + 12. (5 marks) 10. At what point on the parabola y = 3x2 + 2xisthetangentlineparallel totheline y = 10x -2? Use first principles in your solution. (6 marks) 1. Fill in the tables below for each of the following polynomials: [K10] a) f(x)=x²-13x²+3x-9 Degree Type of polynomial b) f(x)=6x4 +7x²-8x+9 Degree Type of polynomial Sign of leading End behaviours coefficient Sign of leading End behaviours coefficient Domain Domain 2. Fill in the table below for the polynomial function: [K9] f(x)=(x-4) (x+1)²(x-5) x-intercepts and behaviour of graph at each x - intercept y - intercept End behaviours 3. Solve the following equation algebraically. Explain your process. [A6], [C3] 0=18x4+87x³+3x²-108x 4. a) Describe the transformations on the cubic function below. Explain your thinking process. [C4] f(x)=7 [(x-5)]³¹-45 b) The point (-9, -2446) is on the transformed function f(x)=7 [Cx-5)]³-45 use the transformation statement the find the original point on the parent function. Justify your answer. [T3], [C2] 5. Determine the values of m and n for f(x)=mx³+20x²+nx-35 given that (x+ 1) gives a remainder of zero, and when divided by (x-2) the remainder is 45. [T5], [C3] 6. Use algebra to determine whether the following function is even, odd or neither. [A6] a) b) f(x)=55x4-x²-78 f(x)=37x¹+93x ctions There are 10 questions in this Assessment of Learning for a total of 60 marks. Show all work for each question. 1. Determine the average rate of change of y in the function y = 2x³ + 7x² + 2x - 3 over the interval [3,5]. (5 marks) 2. Given the function f(x) = 2x² + 3x + 1, a. Use the secant method to find the instantaneous rate of change whenx= 1. (4 marks) b. Use First Principles to find the value of the derivative when x = 1. (4 marks) c. What did you notice? (1 mark) 3. Explain the difference between a secant line and a tangent line. How do they relate to the rate of change of a function? Include a sketch of each type of line in your solution. (6 marks) 4. The path of a baseball relative to the ground can be modelled by the function dur) = -f² + 8 + 1, where dur) represents the height of the ball in metres, and represents time in seconds. a. Find the average rate of change of the ball between 1 and 3 seconds. (4 marks) b. Using the secant method, find the instantaneous rate of change at 2 seconds. (8 marks) 5. a. Evaluate lim (3x³ +7x-16). b. What is the meaning of this value? (2 marks) 6. Evaluate the following limits. x²-16 a. lim X-4 x-4 &r _5r+17 x6x²+2x²-4x b. lim. c. lim A-40 d. lim 3+2 (3 marks) 49+h-7 h y²-8 2y²-7y+12 4 e. lim 2+h A+0 h 2 (2 marks) (3 marks) (4 marks) (2 marks) (3 marks) 7. Find the slope of the tangent line at point (-2,2) on the curve fux) = 2x² + 3x using First Principles. (4 marks) 8. Find the derivative of the function f(x) Principles. (4 marks) = 2 x - 10x + 3 using First 9. Using first principles, determine the equation of the tangent line at point (2.2) on the curve f(x) = x ² = 7x + 12. (5 marks) 10. At what point on the parabola y = 3x2 + 2xisthetangentlineparallel totheline y = 10x -2? Use first principles in your solution. (6 marks)

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The answers of the questions are as follows a Given that fen 1134 3x 9 Since the polynomi... View the full answer