# How do you find the domain and range of f(x)=1/(3x-6)?

Oct 21, 2015

$y \in \mathbb{R} \text{\} \left\{0\right\}$
$x \in \mathbb{R} \text{\} \left\{2\right\}$

#### Explanation:

Finding the Vertical asymptote by making sure that the denominator cannot reach zero.

$3 x - 6 \ne 0$

$3 x \ne 6$

$x \ne 2$

Find the Horizontal asymptote by knowing that when degree of denominator > degree of numerator, H.A = 0.

Therefore, $y \ne 0$

Since there are no other restrictions, $y \in \mathbb{R} \text{\} \left\{0\right\}$ and $x \in \mathbb{R} \text{\} \left\{2\right\}$.