how do i find the domain and range of equations?

Question

example: f(x)=ab.solute value of x-3.

f(x)=square root 36-x^2

g(x)=-2x+2.

how would i know what the domain and range is of these. could i use a graphing calculator to tell me the domain and range??

Answer 1

y = │x-3│

becomes y = x-3 , y = -x+3

clearly I can use any x I feel like and get a y value.
so the domain is the set of real numbers

A nice way to get the range is to graph both lines and use only the part above the x-axis. These two intersect at (3,0) and form a V upwards
the range is any y ≥ 0

f(x) = √(36-x^2)
clearly if we use any value of x such that -6 < x < 6 we would be taking the square root of a negative, which would be undefined.

so the domain is x ≤ -6 OR x ≥ 6
the range is y ≥ 0

the last one is real easy.

in a simple way, the domain is set of all number you can use for x in your function without causing any undefined results,
the range is the set of resulting y values you get from those x's

Answer 2

so what is the answer to the last one?