Question

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

Answer 1

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`