1. 1D. 11. 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 coefcient of -5 e. has a 1y-intercept at 10 What are two different polynomials that Rod could be thinking of? Are those the only possible answers? [IE marks] Create a question similar to #'i above, and provide a description of how a teacher could check that a student's response was correct. [3 marks] Describe a function that has a. adomain of{x E R | 2 5 x 5 1D}. and b. arangeof{yER|55y51[l}. 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] Consider polynomial functions in the form fix} 2 ax\" + 2:. 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. [5 marks] Fully factor the following polynomials. Explain your thought process with your solution. a. x} = 2x3 25x2 + 53x 3D [3 marks] b. fx) = x3 + 3x 4 [3 marks] Sketch the graph of the function x] 2 {x 4](x + 1)2{x 5]. Explain your thinking. [4 marks] Solve the equation 53\" + x = 5x3 + 2x2. [4 marks] Describe the transformations on the guartic function x} 2 14l3lx 5)]4 45. [2 marks] Determine the values of m and n for fix] 2 mx3 + 12x2 + as 3 given that the remainder when dividing by [x + 3) is zero, and when divided by (x 2) the remainder is 85. [5 marks] Use algebra to determine whether the function fix} = 22x3 15's is even, odd, or neither. [4 marks] Graph the function x} 2 2x2 + 2x + 4 and its reciprocal on the same or separate axes. Explain your thinking. [5 marks] 2x+3 x-E 12. Sketch the graph of the function f[x] = with the function. [5 marks] _ Describe its features and their relationship 13. Solve the inequality E at: 2"\" x-3 _ {PIT _ Include an interval chart in 1vour solution. [4 marks] 14. Solve the inequality Ex 3 5 2x + l 5 1?: 3. Explain your solution in words. [5 marks] 15. Considers box with dimensions 3 cm x 5 cm x 11 cm. If all of its dimensions are increased by x cm, what values of I will give a box with a volume between 31313 cm3 and son cma? [5 marks]