SHORT ANSWER: 1. Solve by factoring (must show synthetic or long division as part of your answer) : 2x3 + 3x2 - 8x -12 = 0. Identify the integral and rational zero test values to start your work. (5 marks) Mu yo 1. 2. Write the equation of the rational function in the form y : f(x) that has the g ( x ) following characteristics. Explain how each feature is used to create the function. (5 marks) . Vertical asymptote at x = 1 Point of Discontinuity at | -4, . x-intercept at (4, 0) Math 30-1 Unit 1 Exam Center for Learning at Home Page 5 of 9Numerical Response #3 The graph of y = x3 is transformed by a vertical stretch relative to the x-axis by a factor of 3, reflected in the y-axis, and translated horizontally 3 units to the of a and b is left. The point (2, 8) becomes the point (a, b) after the transformation. The sum 6. Which of the following is a true inverse of y = 3x2 + 2? A. yl = x - 2 3 C. y ' = 1 x-2 3 B. y-1 _ Vx - 2 3 D. y- 1 _ #Vx - 2 3 7. If g(x) = -af [b(x - c)] + dis the transformed function y = f(x), what will the new value of y on the transformed function become? A. ay - d B. -ay - d (1.0) 36 ba's C. ay + d D. -ay + d 8 . A restriction on the domain of f(x) = x2 + 4 , such that its inverse is also a function, could be: A. x 2 -4 B. X20 C. XS2 D. XS 4 benistdo al Tabnieman amse sAT (x)9 V erIT Numerical Response #4 Assuming a minimum degree, an equation for the polynomial function on the right is P(x) = a(x + 1)(x - c)d. The values of a, b, c, and d are and 30 20 (0, 12) 10 -4 -2 2 -10 - -20Dyl Hebs LEARNING @HOME St. Paul's Academy EXCELLENCE IN ONLINE EDUCATION Math 30-1 Unit 1 Exam Multiple Choice: Select the best answer and write the capital letter of your choice onto the Unit 1 Exam Answer Sheet. 1 . Compare the graph of y = (-x) + 4 to the graph of y = x3. A. Reflection in the y-axis and a vertical translation of 4 units up. B. Reflection in the x-axis and a vertical translation of 4 units up. C. Reflection in the y-axis and a horizontal translation of 4 units left. D. Reflection in the x-axis and a horizontal translation of 4 units left. 2. The graph of y + 2 = -3f\\ (x +5) is the image of the graph y = f(x) after several transformations. Which statement about how the graph of y = f(x) was transformed is FALSE? A. The graph was reflected in the x-axis B. The graph was horizontally stretched by a factor of 2 C. The graph was translated 2 units down D. The graph was reflected in the y-axis Numerical Response #1 The point (8, -3) is on the graph of y = f(x). If the transformations within y = f(2x - 4) is applied, then the new point is (k, -3). Determine the value of k. 3. If the graph of y = f(x) is stretched vertically relative to the x-axis by a factor of , and stretched horizontally relative to the y-axis by a factor of -, the function would become A. X =75 5x B. y = - f [5x] C. y = 5f -x D. y = =f [7x]