Finding the domain/range of a funtion help

Can someone explain step by step how to identify them?

For example:

f(x)= (x-4)^2 - 16 , where x is any real number and x>0
g(x)= 8/(1-x), where x is any real number and x<1

a) Find the range of f


Thank you

Can someone explain step by step how to identify them?

For example:

f(x)= (x-4)^2 - 16 , where x is any real number and x>0
g(x)= 8/(1-x), where x is any real number and x<1

a) Find the range of f


Thank you

For your first example, a graph may help (think about the minimum point).

For g(x), a graph may also help.

For a lot of these questions testing the values of f around the endpoints of the domain (eg something like 0.99 for g(x) as well as 'large' values (infinity, -infinity) may give you an idea of what the range is.

sketch just the shape of the graph for all reals
mark the coordinates of the minimum point
"throw" away the graph for which x<0
then you will see the graph lives in y for every value greater or equal to -16

I did draw it (may/probably) wrong because I got: when x=0, y=0.. so I assumed the range would be greater than 0.