In a digital filter, one of the parameters in its difference equation is given by the formula

a) Show that the above formula has one horizontal and one vertical asymptote.

b) show that the graph of 11 against x passes through the origin'

c) By attempting to find the turning points of the above function, show that there aren't any.

d) Sketch the graph of Y against x.

e) From the resulting sketch, find:

i) The value that y approaches to whenever r increases to a very large number.

ii) The sampling interval T if, as the parameter y increases, x is required to approach the value -2.