Question

Let y=f(x) be a function with domain=[-7,8] and range=[-12,9]. Find the range of the function y=-f(2x)

Answer 1

Can't tell. If f(x) is linear, then just multiply the range by -2 to get [-18,24]

For example, if f(x) = 7/5 x - 11/5
then -f(2x) = 22/5 - 14/5 x
and the range is indeed [-18,24]

But, if f(x) is not linear, say

f(x) = 7/5 x^2 - 403/5 then
-f(2x) = 806/5 - 28/5 x^2
and the range is now [-986/5,-566/5]