domain and range?

Question

state the domain and range of the following function:

f(x) = absvalue(x + 1) + absvalue (x - 3)

Answer 1

This function is defined for every real x, so it's domain is R.

For the range, we have:

if x <=-1, f(x) = -x -1 - x + 3 = -2x + 2 So, f(x) is in [4, oo)
If x is in (-1, 3), then f(x) = x +1 -x + 3 = 4, constant.
If x >=3, then f(x) = x +1 + x -3 = 2x + 2 s, f(x) is in [4, oo)

So, the range is [4 , oo)

The graph of the function is something like sketched below

\ ----------------------------- /
\ -------------------------- /
\ ------------------------- /
4 \-----------------------/
-1 --------------------3

Answer 2

domain: all real numbers
range: easiest way is to graph or find domain of its inverse
x=|y+1|+|y-3|
solve for y, find domain of x