show all working and include graphs

1. Find the domain of the function f (x) = +2 15 2x 2. Graph the piecewise function f (x) = 2x-3, if x 51 3. Use the graph to estimate the intervals where the function increases and decreases. Estimate the coordinates of the local max/min 4. Given f (x) = -Vx-2 +1, a) State the toolkit function y = g(x ) related to > = Rx). b) Describe the sequence of transformations leading from y = g(x) to y = f(x). c) Sketch toolkit function and all transformations on the same set of coordinate axis, 5. a) Find the inverse function for f(x) = 1 - 3x. b) Check that -3 0 Sketch both graphs on the same set of axis. d) Describe the relationship between the graphs of original and inverse functions