`y=-4/(x+4)+3` Graph the function. State the domain and range.

We are asked to graph the function `y=(-4)/(x+4)+3 ` :

Note that this is a transformation of the function y=1/x whose graph is a hyperbola. The transformation consists of a reflection over the horizontal axis, a translation 4 units left, a translation 3 units up, and a dilation of factor 4.

There is a vertical asymptote at x=-4 and a horizontal asymptote at y=3.

The domain is all reals except -4 and the range is all reals except 3.

The graph:

Comments

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