`g(x)=(5x)/(2x+3)` Graph the function. State the domain and range.

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embizze eNotes educator| Certified Educator

We are asked to graph the function `y=(5x)/(2x+3) ` :

The graph has a vertical asymptote at x=-3/2. The graph has a horizontal asymptote at y=5/2.

The domain is `RR-{-3/2} ` while the range is ` RR-{5/2} ` .

We can rewrite the function using division as `y=(-15)/(4(x+3/2))-5/2 ` . Using the hyperbola y=1/x as the base function, the transformation is a translation 3/2 units left, 5/2 units down, a reflection across the horizontal axis, and a vertical dilation of 15/4.

The graph: