# How do you find the domain and range of g(x)= (3x)/(2x-5)?

Jul 19, 2015

For the domain there is only the restriction that $x \ne 2 \frac{1}{2}$
This would make the numerator $= 0$

#### Explanation:

In the "language" we say:

${\lim}_{x \to 2 \frac{1}{2}} g \left(x\right) = \infty$ and $x = 2 \frac{1}{2}$ is the vertical asymptote

As $x$ gets larger the function will tend to look more and more like

$\frac{3 x}{2 x} = 1 \frac{1}{2}$ without quite getting there, or:

${\lim}_{x \to \infty} g \left(x\right) = 1 \frac{1}{2}$ or $g \left(x\right) = 1 \frac{1}{2}$ is the horizontal asymptote

So the range has as only restriction $g \left(x\right) \ne 1 \frac{1}{2}$

graph{3x/(2x-5) [-10.98, 21.04, -5.92, 10.1]}