f(x) has not been provided, so I have to guess at a definition of f(x) to suit the question. Let a, b, c, d be 2, 3, 4, 5 respectively.
b) Start with 4y+3xy-15x=22 where y=f(x).
y(4+3x)=22+15x, y=(22+15x)/(4+3x),
y=(15x+22)/(3x+4)=(15x+20+2)/(3x+4),
y=5+2/(3x+4), so f(x)=2/(3x+4)+5 in the required format.
c) The parent equation is y=1/x which has a vertical asymptote at x=0. This asymptote now becomes x=-4/3 which is a left shift of 4/3 (displacement of x-axis). This is the first transformation. The horizontal asymptote of y=1/x is the x-axis (y=0). (This changes as we'll see.) The asymptotes divide the graph into two--a negative part and a positive part.
The next transformation is a vertical dilation of 2 (the numerator) which expands the graph vertically.
The final transformation shifts the graph vertically 5 units. This affects the horizontal asymptote so that it is now at y=5 instead of y=0. The two asymptotes are now x=-4/3 and y=5 and, as with the parent function, these split the graph into two halves.
The purple hyperbola is y=1/x, the parent. The red hyperbola is f(x). The asymptotes are shown as green and blue lines. You can see how the coloured asymptotes form axes in relation to f(x) just as the x- and y-axes did for y=1/x.