Let y = f(x) be a function with domain D = [−6, 10] and range R = [−8, 12]. Find the domain D and range R for each function. Assume f(6) = 12 and f(10) = −8. (Enter your answers using interval notation.)
a) y = −2f(x)
b) y = |f(x)|
c) y = f(x + 2) − 3

Question

Let y = f(x) be a function with domain D = [−6, 10] and range R = [−8, 12]. Find the domain D and range R for each function. Assume f(6) = 12 and f(10) = −8. (Enter your answers using interval notation.)
a) y = −2f(x)
b) y = |f(x)|
c) y = f(x + 2) − 3

anonymous · Answer

for the first one, the domain doesn't change, since it is still $f(x)$ but the range will change because you will multiply all your outputs by $-2$ and so the range will be $[-24,16]$

anonymous · Answer

second one, again the domain doesn't change, but all the outputs will now be positive, so the range will be $[0,12]$

anonymous · Answer

for the third one, since the smallest number you can use is $-6$ as an input, we can solve $x+2=-6$ so get $x=-8$
largest is 10 solving $x+2=10$ gives $x=8$ so the domain of $f(x+2)-3$ will be 
$$[-8,10]$$ since we are then subtracting 3, range will be $[-11,9]$

anonymous · Answer

for c [-8,10] did not work