How do you find the domain and range of #y=-abs(x +4)#?

1 Answer

Answer:

D: #x in RR#; R: #y<=0#

Explanation:

Domain - the list of all permissible #x# values

There are no values of x that are impermissible and so the domain of #x# is all real numbers, which we can write in a number of ways, with one way being

#x in RR#

Range - the list of all resulting #y# values

When we evaluate an absolute value, we will always get a value that is at least 0. In our current question, when #x=-4, abs(-4+4)=0; x=-5 and x=-3# returns 1, and so forth.

So we have a positive number coming from the absolute value brackets to which we are multiplying a #-1#, which will make the values negative. And so the possible values of #y# start at 0 and decrease towards #-oo#. We can write that as:

#y<=0#