a. D= (x ER|-85x4 - 2x2 - 3? a. (x - 1)(x + 1)(x -3) C. (x + 1)(x2 - 3) b. (x - 1) (x + 3) none of the above 7. Based on the graph of f(x) = x4 - 2x' + 3x + 2 shown, what are the real roots of x4 - 2x3 + 3x + 2 = 0? 4 2 -2 0 a. 2 c. impossible to determine . -2, -1, 1, 2 d. no real roots 8. Which of the following graphs of polynomial functions corresponds to a cubic polynomial equation with roots -2, 3, and 4? a. 4 -2 0 b. d. N 2 0 -2 2 9. What is the equation of the horizontal asymptote of f(x) = -7, 2x + 10- a. y = 0 C. x= 0 b. y = 5 d. x = 5 x +2 _x+7 10. Solve the equation x _7 - x+ 3 a. x= -11 C. x = 7, x= -3 b. d. no solution * = 55 11. Which of the following functions has exactly one vertical asymptote when graphed? a. Ax) = - 6 C. Ax ) =- 6x - 18x x2 - 3x X b. 6x Ax) = 2_ d. B and C x2 - 3x 12. If a function is of the type y = A sin( B(x - C) ) - D and the amplitude is 2, there is an horizontal stretch of 2, and a shift down of 3, what are the values of A, B, C and D, respectively? a. 0.5, 3, 0, 2 c. 0.5, 0, 2, 3 b. 2, 0.5, 3, 0 d. 2, 0.5, 0, 3 13. Which is the first transformation that should be applied the graph of (x)=10g10* to graph A(x)=410g 10 (x -5)+3?3:48 0 X TA MHF4U... A Talenta Academy Advanced Functions (MHF4U) K/U T/I C Total Marks (%) 122 120 /14 122 178 FINAL ASSIGNMENT Name:. .. ..... Date:.. . . . ..... . . . . .. Teacher: Mr. Mahalingam Part A: Multiple Choice [K/U-15] Identify the choice that best completes the statement or answers the question. 1. Which of the following is an odd function? a. y= x(x+x) C. y=-5x-(x-2) y = -3x(x-2) d. y = 2x(x-x) 2. An equation representing a function that extends from quadrant 3 to quadrant 1 is a. y= (x-1 )(x +2 c. y=-2(x -3)'(x + 4) . y= -2x(x -1)(x -2) d. y= (x-1)' (x+3)5 3. Which equation describes the function rule "subtract 5 from the input and then multiply by 2 to find the output"? a. 2y = x-5 C. x = 2y-5 b. y = 2(x - 5) d. y = 2x- 5 4. State the domain of the following piecewise function. D = (x ER| -85x) + 3 [K/U-3] 26. a) Write the equation of the function with the zeros at -4, -1, 2 (order 2), and the leading coefficient is 1. [T-6] a) Graph the function b) Determine the number of degree, c) type of function d) number of turning points e) Quadrants f) Interval of positiveegative of functions g) the end behaviours of the polynomial function. 7 29. Prove sec x + tan x = cos x [T/1-4] (1 - sin x) 30. Find the exact value of cos 12 [ A-4]3 of 10 9. What is the equation of the horizontal asymptote of f(x) = -7, 1 2x + 10? a. y= 0 C. X = 0 b. y = 5 d. x = 5 x+ 2 _x+7 10. Solve the equation x _7 - x+ 3 a. x =-11 C. x = 7, x= -3 b. d. no solution * =- 55 11. Which of the following functions has exactly one vertical asymptote when graphed? a. Ax) = 6 C. x2 - 3x Ax) = Ox" - 18x b. Ax) = = 6x d. B and C x2 - 3x 12. If a function is of the type y = A sin( B(x - C) ) - D and the amplitude is 2, there is an horizontal stretch of 2, and a shift down of 3, what are the values of A, B, C and D, respectively? a. 0.5, 3, 0, 2 c. 0.5, 0, 2, 3 b. 2, 0.5, 3, 0 d. 2, 0.5, 0, 3 13. Which is the first transformation that should be applied the graph of A(x)=10g10* to graph Ax)=410g 10 (x -5)+3? a. Vertical stretch by a factor of 4 b. Horizontal translation 5 units to the right c . Vertical translation 3 units up d. Vertical compression by a factor of 4 14. Express 27 =3 in logarithmic form. a. log3 27=3 C. 10827 3= = b. log: 3 =27 d. log3 3=27 15. State the law of logarithms used to rewrite log, 32-log, 8 as log, 4. a. Difference law of logarithms c. Power law of logarithms b. Product law of logarithms Quotient law of logarithms 3 Part B: SHORT ANSWER AND PROBLEM SOLVING. SHOW EVERY STEP OF YOUR WORK TO GET FULL MARK. Please, answer all questions in the space provided. Show all your work with every steps how you found your answer to get full mark. 16. Determine the zeros, leading coefficient, and an equation for the graph of the polynomial function shown below. [A-4) 25 20 10 17. What is the equation of the function of Sine that has an amplitude of 4, a period of 2x and has a point at (0,2)? [C-3]7 8 of 10 29. Prove sec x + tan x = cos x [T/1-4] (1 - sin x) 30. Find the exact value of cos 12 [ A-4] 8 30. Sketch a graph of y = 2 cos (2x + 90 ) + 1 for -2n S x S 2x, [A-7] and state the following: the amplitude, period, equation of the axis