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

1 Answer
Jan 20, 2018

Answer:

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]#