The following sentences in First Order Logic contain existential quantifiers $().$ Use skolemization on each sentence to remove the existential quantifier by introducing new skolem constants or skolem functions.

There exists a musician with fans.

$$x$$y $[$Musician$($x$)$ FanOf$($y$,$ x$)]$

All fans of a movie actress saw one of her movies.

$$x$$y $[$Actress$($x$)$ FanOf$($y$,$ x$)->$z$[$Movie$($z$)$ Act$($x$,$ z$)$ Watched$($y$,$ z$)]]$

Every game designer designs at least one game.

$$x$[$Designer$($x$)->$y$[$Game$($y$)$ Design$($x$,$ y$)]]$