Knowledge (15 marks} Multiple Choice {2 marks each} -Identify the choice that best completes the statement or answers the question and then provide a reason or mathematical rationale on the line below each question. 1. Determine the nmnber of real solutions when solving this equation: I] = r (n+5)2 (Jr3J1. a. 4 c. 3 b. 2 d 5 2 . The function 3? = {11) {12) {13) is positive on the interval: as E (1,2}und IE (3.130] x E (2, 3} x E { m. Bond 1' E [2. 3] x E (2, 3} nose 3. Width of the following represents a cubic that enters in Quadrant 3 and exits in Quadrant 1? a. {x 1f( 33: 2) e. [x + 1)Z[3x + 2}1 b. (x + 1]\"[2 317) d. ( x + 1323:: + 2) 4. Which of the following is not a member of the family of cubic functions with roots: (-3,0), (4, 0) and (1,0)? a. y = 5(x+4)(x-3)(x+1) c. y= -(x -1)(x+3)(x-4) b. y = 1/2 (x-4)(x+3)(x-1) d. y=-3x +6x +33x - 36 5. Which function below satisfies the properties of an Odd Function? a. (x + 1)(x - 1)2 c. y = x (x+ 1) b. - (x + 1) (x + 5)3 d. (x + 1) (3x + 2) True/False Indicate whether the statement is true or false. 6. If the solution to P(x) = 0 is x = 8, then (x+8) is a factor of the polynomial P(x). 7. The only real solution to this equation 0 = - (x - 5)(x + 9)is x =5. 8. The test to see if a function is in fact an 'odd function' is: f(-x) = -f(x). 9 When forming a family of polynomial functions, the intercepts are all the same for every function that belongs to the family. 10. If an even degree function is in fact an 'even function', it has point symmetry about the origin.\fThinking ti: Inquiryr {'5' marks} 13. A quartic function has zeros HS, -2, and 3 (order 2). a) First, determine a general equation for ALL members of this polynomial family. b) THEN, determine the specic fanniI},r member that has the point { -4 , 491 J. Use simplified, exact fraction 1values when necessary. {3 marks} 14. The specifications for a cardboard box state that thewidth is 4cm less than length. and the height is 5" cm more than twice the length. Use technology {Desmos? You Choose] AND include ALL screensl'tots used in solving this problem. (4 marks] a) Identify the variables you will use and create an equation for the 1volume of the box. length - Width - Height- b) Find the possible dimensions for a volume of 9922.5 cm? and round to the nearest tenth of a centimetre