# What is the domain and range of y = |x| + 5?

Jul 3, 2018

#### Answer:

The domain is $x \in \mathbb{R}$. The range is $y \in \left[5 , + \infty\right)$

#### Explanation:

The function is

$y = | x | + 5$

For the absolute value, $x$ can take any value.

Therefore, the domain is $x \in \mathbb{R}$

The minimum value of $y$ is when $x = 0$

$\implies$, $y = 5$

And due to the presence of the asolute value, $y$ can take only positive values as

$| - x | = x$

Therefore, the range is $y \in \left[5 , + \infty\right)$

graph{|x|+5 [-56.73, 60.37, -20.6, 37.95]}