The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. which statement about the range of both functions is true?

a. the range is the same for both functions: {y | y is a real number}.\
b. the range is the same for both functions: {y | y > 0}.
c. the range changes from {y | y > 0} to {y | y > 2}.
d. the range changes from {y | y > 0} to {y | y > 6}.

i need quickly !

Range is how far theh y values run, up to down

so

translation up, z units, add z to whole function
translateion right c units, minus c from every x
so
6 to right
2 up
minus 6 from every x and ad 2 to everybody

f(x)=|x-6|+2
the range needs some logic
so find the smallest and largest value of y or f(x)
absolute value make thing positive, so making an extremely large negative number gives a large positive number
make absolute value 0 then f(x)=2, min is 2
max is infinity

range changes  from y>0 to y>2
C is answer