Assuming that the cost for this linear version of Lucas sequence is exactly 3x + 2. Calculate the Big Theta bound. While it should be linear, provide witnesses for Big O and Big Omega to establish...

Assuming that the cost for this linear version of Lucas sequence is exactly 3x + 2. Calculate the Big Theta bound. While it should be linear, provide witnesses for Big O and Big Omega to establish that the code is Big Theta, and demonstrate the bounds on a graph.