As for the domain, the only restriction comes from the logarithm. The argument of a logarith must be strictly positive, so we have
[tex] x-2>0 \iff x>2[/tex]
As for the range, we have:
- The range of [tex]\log(x)[/tex] are all real numbers
- If we change to [tex]\log(x-2)[/tex] we're translating the function horizontally, so the range remains the same
- If we change to [tex]\log(5(x-2()[/tex] we're stretching the function horizontally, so the range doesn't change
- If we change to [tex]\log(5(x-2))+1[/tex] we're translating the function 1 unit up, but the range is already all the real numbers, so it doesn't change.
