1. Consider the functions f(x) = %and glx) = + 2. Describe the transformations that occurred from g(x) to f(x). a. A reflection in the y-axis, a horizontal translation 3 units to the left and a vertical translation 2 units down. b. A reflection in the y-axis, a horizontal translation 3 units to the right and a vertical translation 2 units up. . A reflection in the x-axis, a horizontal translation 3 units to the left and a vertical translation 2 units down. d. A reflection in the x-axis, a horizontal translation 3 units to the right and a vertical translation 2 units up. 2. The point of discontinuity on the graph f(x) = 1:;;5 occurs at: +dx5 a. ( 5,%] 1 b. [4, T) c. (0,1) d. There are no points of discontinuity Use the following information to answer guestions 3 and 4. pX gx) = +5 . . . Trg 152 rational function where p and g are natural numbers. 3. The vertical asymptote for g(x) is: a x=4g b x= q x =7qg d. x=J;- 4. The horizontal asymptote for g(x) is: a. y=p b PET o W= =5 d y= = 5. If the point of discontinuity of the graph for the function f(x) = % can be represented X Bx+ by (a, b), then the value of @ + b to the nearest hundredth is 1. (a) Use a calculator to sketch each of the following rational functions. i) y = - x+2 ii) y = x+2 x -3 iii) y = x +3x+2 x+2(b) Complete the table. 1 ) 7 +2 ii) y = iii) y = - x +3x+2 *+2 Vertical Asymptote Horizontal Asymptote Point of Discontinuity Domain Range x-intercept y-intercept 2. Determine the equations of the vertical and horizontal asymptotes of each of the following functions. Show your work. a) y = b) y =4x-5 x +2 c)y =*+5x+6 x+6 d) y = 2_4265 +x 25x+12 x=3 3. Consider the function defined by f(x) = a) Algebraically determine the coordinates of the point of discontinuity of the graph of the function. (2 marks) 2+ 25x+12 = 0 and the x-intercepts of the x=3 b) Describe the relationship between the roots of the equation graph of f{x). (1 mark) 2 +x"25x+12 = (). Explain and show how you determined the solution. (2 marks) c) Solve the equation d) Sketch the graph including any intercepts, asymptotes, and the point of discontinuity. (2 marks) 1 kxc 4. Determine an equation in the form f(x) = for a function with a vertical asymptote at x = 2anda y-intercept of %. (2 marks) " s x+5 2x+7 5. Solve the rational equation