The graph of tangent is continuous (i.e. has no breaks) true or false

Question

Is it that the line of the tangent in the graph will be a continuous or broken 

Answer 1

FALSE.  Consider, for example, what happens near π/2.  As x approaches π/2 from the left, tan(x) approaches infinity.  But as x approaches π/2 from the right, tan(x) approaches negative infinity.  So there is a break at π/2.