The tangent function

1. use the scrollbar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the period phase shift and positions of asymptotes (in red)of f(x)? Now change a , how does it affect the graph?
   
   
2. set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to pi/|b|. How does b affect the graph of f(x)?How does it affect the asymptotes?
   
   
3. set a=1,b=1,d=0 and change c starting from zero going slowly to positive large values. Take note of the shift, is it left or right, and compare it to -c/b.
   
   
4. set a=1,b=1,d=0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to -c/b.
   
   
5. repeat 3 and 4 above for b=2,3 and 4.
   
   
6. set a,b and c to non zero values and change d. What is the direction of the shift of the graph?
   
   
7. What parameters affect the positions of the asymptotes? Explain algebraically.