y=(-5x+2)/(4x+5) Graph the function. State the domain and range.

We are asked to graph the function y=(-5x+2)/(4x+5) :
There is a vertical asymptote at x=-5/4 . Since the degree of the numerator is the same as that of the denominator, there is a horizontal asymptote at y=-5/4.
Thus the domain is RR-{-5/4} while the range is RR-{-5/4} . (An alternative way to write the domain and range is (-oo,-5/4)uu(-5/4,oo) , or x ne -5/4, yne -5/4 .)
The y-intercept is 2/5 and the x-intercept is also 2/5.
Using division we can rewrite the function as y=33/(16(x+5/4))-5/4 ; if we take the base function to be y=1/x, then the graph of the transformation is shifted left 5/4 units, down 5/4 units, and has a vertical dilation of factor 33/16.
The graph: