Angular2 filter observable with switchMap - asp.net-web-api

Question

I'm doing a term search using Angular2 and WebAPI using a method described in numerous Angular2 tutorials.
In my service:
search(term: string): Observable<UserList[]> {
return this.http.get(this.userSearchUrl + term)
.map((response: Response) => response.json())
.catch(this.handleError);
}
In my component:
ngOnInit(): void {
this.users = this.searchTermStream
.debounceTime(300)
.distinctUntilChanged()
.switchMap((term: string) =>
term ? this.userService.search(term) : Observable.of<UserList[]>([]))
.catch(error => {
console.log(error);
return Observable.of<UserList[]>([]);
});
}
What I would like to do on the service side is keep track of the last search. So if my initial search is "b" and then I search for "bo" you should not have to make another call to WebAPI since we already have the results we need we just need to filter down further. I assume that doing that with Observables is out of the question/difficult since you subscribe to a stream but I don't know much about Observables yet. I thought maybe doing it with a promise might be easier, but I'm not sure how to handle the component side of it like Subject() and switchMap() which seem to only be for Observables
This is something like what I would like to use on the service side:
searchPromise(term: string): Promise<UserList[]> {
if (this.lastUsedTerm.length > 0 && term.indexOf(this.lastUsedTerm) == 0) {
this.lastUsedSearch = this.lastUsedSearch.then(x => x.filter(z => z.firstName.startsWith(term)));
}
else {
this.lastUsedSearch = this.http.get(this.userSearchUrl + term)
.toPromise()
.then((response: Response) => response.json())
.catch(this.handleError);
}
this.lastUsedTerm = term;
return this.lastUsedSearch.then(x => x.filter(z => z.firstName.startsWith("bob")));
}