1. Draw the graph of the function f(x) = 2[x] for the domain -2 < x ≤ 1.
2. Consider the function f(x) = 1/3x + 2.
(a) Find the inverse of and name it . Show and explain your work.
(b) Use function composition to show that and are inverses of each other.
(c) Draw the graphs of f(x) and on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.
3. A swimmer floats on the surface of a completely filled 10-foot deep pool for 5 seconds. He then takes 3 seconds to swim to the bottom of the pool and 2 seconds to return to the surface, where he then floats for another 5 seconds. After that, his watch slips off and he swims halfway to the bottom to grab it. It took him 1 second to grab the watch and another 1 second to swim back to the surface.
Draw a graph that models the swimmer's depth below the water's surface over time.