The function f(x)=tanx where x∈(−π4,π4).
Let's try to draw the function in a graph.
Here not that in the domain i.e. x=π2 is not present. Domain is x∈(−π4,π4) for which the function doesn't have any breaks.
Hence in the given interval the function tanx is continuous or we can say the function is continuous at each and every point in its defined domain.
Also just observation, the function's increasing nature can also be noted.