Question

How do you find the domain & range for `f(x)= -sin(x-π)-1`?

Answer 1

Domain: `xin RR`
Range: `[0,-2] in RR`

Explanation:

`sin(x-pi)` has the same domain and range as `sin(x)`; namely domain: `RR`; range `[-1,+1]`. Subtracting `pi` from `x` within the argument of `sin` only shifts the pattern to the left by `pi`.

`-sin(x-pi)` has the same domain and range as `sin(x-pi)`; the point are simply reflected in the X-axis.

`sin(x-pi)-1` has the same domain as `-sin(x-pi)` but the range is reduced by `1`; that is the range becomes `[-2,0]` instead of `[-1,1]`