Calc Problem 1

Given figure 1 to be the graph of the function f(r) with three points labeled and two sets of blank axis. The domain and range of f(r) is R and [-4, co), respectively. (a) Let g(x) = 2f(-2x - 4) + 1. Draw the graph of g(r). Make sure to clearly label where the three labeled points on the graph of f(x) are translated to on g(r). (b) Give the domain and range of g(r). (c) Suppose we restrict the domain of f(x) to [2,8). Draw the graph of f-(x). Again, make sure to clearly label the points on your drawing that correspond to the labeled points in this domain. (d) Give the domain and range of f-1(x). (e) What property does the restricted domain version of f from part (c) have that allows us to define the inverse as a function