Please provide clear explanation. Thank you.

For each statement, explain why it must be true, or use an example to show that it can be false. . If y=f(x) has a horizontal tangent line at x=1 then y=g(x) , where g(x) =f(x-1)+1 , has a horizontal tangent line at x =2 . A tangent line always has exactly one point in common with the graph of the function.