A functional isomer of 1-butyne is 

Functional isomerism is the type of isomerism in which molecules have the same chemical formula but having different functional groups.

1,3-butadiene and 1-butyne have the same chemical formula but they have different functional groups:

$$\begin{gathered} \underset{1,3-\mathrm{butadiene}}{\underbrace{{\mathrm{CH}}_2=\mathrm{CH}-\mathrm{CH}={\mathrm{CH}}_2}} \\ \underset{1-\mathrm{butyne}}{\underbrace{\mathrm{HC}\equiv \mathrm{C}-{\mathrm{CH}}_2-{\mathrm{CH}}_3}} \end{gathered}$$