Question

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

Answer 1

The domain is all real numbers.
The range is `[-1,oo]`

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 `2abs(x+1)`. We see that we can do so when `x=-1`.
`y=2abs(x+1)-1`
`y=2abs(-1+1)-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 `[-1,oo]`