firebase.database is not a function

i solved this issue by giving the url in the constructor firebase.database('https://123.firebaseio.com')

A bit late to the party, but in case some one wanted to know the syntax in angular, (or Ionic 4) just add this to your .module.ts file (Note, as peterb mentioned, the /database import)

import { AuthService } from './auth.service';
import { AngularFireAuthModule } from 'angularfire2/auth';
import { AngularFireDatabaseModule } from 'angularfire2/database';

@NgModule({
  imports: [
    AngularFireAuthModule,
    AngularFireDatabaseModule,
    AngularFireModule.initializeApp(environment.firebase),
  ],
  providers: [
  ]
})

I ran into this with Ionic and it turned out that I wasn't including everything when using the latest Firebase Client. If you've included Firebase as firebase-app, then the Database and Auth pieces need to be required separately since they aren't bundled when including Firebase in this way.

Add the following to your index.html after you include firebase-app.js

<script src="https://www.gstatic.com/firebasejs/3.1.0/firebase-auth.js"></script>
<script src="https://www.gstatic.com/firebasejs/3.1.0/firebase-database.js"></script>

Obviously you don't need to use the CDN, you could use bower (probably the preferred way with Ionic) or NPM with Browserify.

// Browserify Setup
var firebase = require('firebase/app');
require('firebase/auth');
require('firebase/database');

Snippet below taken from the Firebase Web Setup Docs

You can reduce the amount of code your app uses by just including the features you need. The individually installable components are:

firebase-app - The core firebase client (required).
firebase-auth - Firebase Authentication (optional).
firebase-database - The Firebase Realtime Database (optional).
firebase-storage - Firebase Storage (optional).

From the CDN, include the individual components you need (include firebase-app first)