Unit 1 Assignment 1. Rod says that he is thinking of a one variable polynomial expression...

Transcribed Image Text:

Unit 1 Assignment 1. Rod says that he is thinking of a one variable polynomial expression that has the following characteristics: a. has a degree of 4 b. has three terms c. one of the terms has degree 1 d. one of the terms has a coefficient of -5 e. has a y-intercept at 10 What are two different polynomials that Rod could be thinking of? Are those the only possible answers? Please include an explanation or rationale with your response. [6 marks] 2. Create a question similar to #1 above, and provide a description of how a teacher could check that a student's response was correct. [3 marks] 3. Describe a function that has a. a domain of {xER | 2x 10}, and b. a range of {y ER | 5 y 10}. Your function does not need to be a polynomial or rational function, and it can be described algebraically, as a graph, or in another form. [4 marks] 4. Consider polynomial functions in the form f(x) = ax" +x. Use at least three examples to investigate the relationship between a, n, and the constant finite differences. Explain the steps you took in your investigation and any conclusions you found. [6 marks] 5. Fully factor the following polynomials. Explain your thought process with your solution. a. f(x)=2x-25x2 + 53x-30 [3 marks] b. f(x)=x3+3x-4 [3 marks] 6. Sketch the graph of the function f(x) = (x-4)(x + 1)(x-5). Explain your thinking. [4 marks] 7. Solve the equation 6x + x = 5x + 2x. [4 marks] 8. Describe the transformations on the quartic function f(x) = 14[3(x-5)]-45. [2 marks] 9. Determine the values of m and n for f(x) = mx + 12x + nx - 3 given that the remainder when dividing by (x + 3) is zero, and when divided by (x-2) the remainder is 85. [6 marks] 10. Use algebra to determine whether the function f(x) = 22x-19x is even, odd, or neither. [4 marks] 11. Graph the function f(x) = -2x + 2x + 4 and its reciprocal on the same or separate axes. Explain your thinking. [5 marks] Copyright 2022 The Ontario Educational Communications Authority. All rights reserved. TVO ILC MHF4U Learning Activity 1.15 Unit 1 Assignment 12. Sketch the graph of the function f(x) = with the function. [5 marks] 2x+3 x-5 Describe its features and their relationship 2x+5 13. Solve the inequality Include an interval chart in your solution. [4 marks] 14. Solve the inequality 8x - 3 2x+1 17x-8. Explain your solution in words. [5 marks] 15. Consider a box with dimensions 3 cm x 5 cm x 11 cm. If all of its dimensions are increased by x cm, what values of x will give a box with a volume between 300 cm and 900 cm? [6 marks] Unit 1 Assignment 1. Rod says that he is thinking of a one variable polynomial expression that has the following characteristics: a. has a degree of 4 b. has three terms c. one of the terms has degree 1 d. one of the terms has a coefficient of -5 e. has a y-intercept at 10 What are two different polynomials that Rod could be thinking of? Are those the only possible answers? Please include an explanation or rationale with your response. [6 marks] 2. Create a question similar to #1 above, and provide a description of how a teacher could check that a student's response was correct. [3 marks] 3. Describe a function that has a. a domain of {xER | 2x 10}, and b. a range of {y ER | 5 y 10}. Your function does not need to be a polynomial or rational function, and it can be described algebraically, as a graph, or in another form. [4 marks] 4. Consider polynomial functions in the form f(x) = ax" +x. Use at least three examples to investigate the relationship between a, n, and the constant finite differences. Explain the steps you took in your investigation and any conclusions you found. [6 marks] 5. Fully factor the following polynomials. Explain your thought process with your solution. a. f(x)=2x-25x2 + 53x-30 [3 marks] b. f(x)=x3+3x-4 [3 marks] 6. Sketch the graph of the function f(x) = (x-4)(x + 1)(x-5). Explain your thinking. [4 marks] 7. Solve the equation 6x + x = 5x + 2x. [4 marks] 8. Describe the transformations on the quartic function f(x) = 14[3(x-5)]-45. [2 marks] 9. Determine the values of m and n for f(x) = mx + 12x + nx - 3 given that the remainder when dividing by (x + 3) is zero, and when divided by (x-2) the remainder is 85. [6 marks] 10. Use algebra to determine whether the function f(x) = 22x-19x is even, odd, or neither. [4 marks] 11. Graph the function f(x) = -2x + 2x + 4 and its reciprocal on the same or separate axes. Explain your thinking. [5 marks] Copyright 2022 The Ontario Educational Communications Authority. All rights reserved. TVO ILC MHF4U Learning Activity 1.15 Unit 1 Assignment 12. Sketch the graph of the function f(x) = with the function. [5 marks] 2x+3 x-5 Describe its features and their relationship 2x+5 13. Solve the inequality Include an interval chart in your solution. [4 marks] 14. Solve the inequality 8x - 3 2x+1 17x-8. Explain your solution in words. [5 marks] 15. Consider a box with dimensions 3 cm x 5 cm x 11 cm. If all of its dimensions are increased by x cm, what values of x will give a box with a volume between 300 cm and 900 cm? [6 marks]