sketch the graphs of these relationships. In your analysis include reference to period, aymptotes, vertical and horizontail shifts, and the value of "a"
a) y = tan(x - pi/4)
b) y = 2tan(2x) + 1
This is about transforming the graph of y=tanx. a. Replacing x by x-pi/4 translates the graph pi/4 in the positive direction.
b. replacing x by 2x produces 'stretch parallel to the x axis with scale factor 1/2. Then multiplying by 2 produces stretch scale factor 2 parallel to the y axis. Finally the +1 produces a translation +1 in the y direction.