Question

f(x)=6 for x=1
f(x)=-x+2 for x>1
Need help finding the domain, range and if f is continuous or not.

Answer 1

function is only defined if \(x\geq 1\) so that is your domain

Answer 2

it is not continuous at 1 because \(f(1)=6\) but if you replace \(x\) by 1 in the second formula you get \(-1+2=1\) so they do not meet up there

Answer 3

since \(-x+2\) has a negative slope, the largest it can be is if \(x=1\) and you get 2 but since \(x\neq 1\) for that formula, the domain would be \(y<2\) and \(y=6\)