# How do you find the domain and range of y= 2 |x+1|-1?

Jan 20, 2018

The domain is all real numbers.
The range is $\left[- 1 , \infty\right]$

#### Explanation:

We can easily see that for whatever number we put in $x$, we can always get a $y$ value.

For the range, we have to find the least value possible of $2 \left\mid x + 1 \right\mid$. We see that we can do so when $x = - 1$.
$y = 2 \left\mid x + 1 \right\mid - 1$
$y = 2 \left\mid - 1 + 1 \right\mid - 1$
$y = - 1$

That is the lowest value possible. Now, we can logically see that there is no limit to how large $y$ could be, since the further away $x$ is from -1, $y$ gets larger. (We have covered previously that $x$ could be any real number.)

Therefore, the range is $\left[- 1 , \infty\right]$