How to plot hyperbolic functions in Maple?

Hyperbolic functions are used in the sciences. The hyperbolic sine , sinh x;the hyperbolic cosine, cosh x; and the hyperbolic tangent, tanh x,defined respectively as

sinh x = e^x− e^−x/ 2, x ∈ R
cosh x = e^x + e^−x/2, x ∈ R
tanh x = e^x− e^−x/e^x + e^−x , x ∈ R

How do I show that these three hyperbolic functions are continuous forall x ∈ R using Maple?