The change from \(-3\) to \(4\) is seven, so the rule is \(y=x+7\).

Input minus seven gives output zero. Smaller inputs give negative outputs, while larger inputs give positive outputs.

For example, input \(-1\) gives output \(6\), disproving the claim about every negative input.

Answer

\(y=x+7\). Outputs are negative for \(x<-7\), zero for \(x=-7\), and positive for \(x>-7\). Negative inputs do not always give negative outputs.