# What is the domain and range of y = log(2x -12)?

Jun 7, 2018

Domain $\left\{x | x > 6\right\}$ in interval notation $\left(6 , \infty\right)$

Range $\left\{y | y \text{ is } \mathbb{R}\right\}$ in interval notation $\left(- \infty , \infty\right)$

#### Explanation:

$y = \log \left(2 x - 12\right)$

input of the log functions must be greater than zero:

$2 x - 12 > 0$

$2 x > 12$

$x > 6$

Domain $\left\{x | x > 6\right\}$ in interval notation $\left(6 , \infty\right)$

As input numbers get closer and closer to 6 the function goes to $- \infty$ and as input gets larger and larger the function goes to $\infty$

Range $\left\{y | y \text{ is } \mathbb{R}\right\}$ in interval notation $\left(- \infty , \infty\right)$

graph{log(2x -12) [-10, 10, -5, 5]}