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

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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:



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