Problem 2 (20pts). Below is a graph of a linear transformation of f(x) = =]. a) (3 pts) Draw a sketch" of the original function f(x) before transformations. b) (5 pts) Write an equation for this graph. c) (2 pts) What is the vertex of this graph? d) (4 pts) Describe the domain and range. e) (5 pts) Explain how you can determine the vertex from your equation and why that is the highest (maximum) point on the graph. f) (2 pts) What number in your equation explains the steepness and direction of the graph? "Make a rough sketch by hand! Do not submit something from an online graphing tool. 10 -5 -10 -5 5 10 -5 10Problem 3 (20pts). Use the function r(x) = I - 31 - 4 x - 2 for the following: a) (6 pts) Sketch" the function, label the intercepts, and include asymptotes. b) (4 pts) Describe the domain. c) (6 pts) Determine two functions f and g such that r(x) = (2 d) (4 pts) Describe the domains of your f and g functions. "Make a rough sketch by hand! Do not submit something from an online graphing tool. - 3x - 4 r(x) = x x - 2 Problem 4 (15pts). Given the functions f(x) = v7x + 2 and g(x) = 2x- - 9: a) (5 pts) Calculate fog(2) and go f(2). b) (5 pts) Find h(x) = fog(x) and j(x) = go f(x) c) (5 pts) Decompose h(x) into two functions s(x) and t(x), which are different than f(x) and g(x), so that h(x) = sot(x)