Angular 2+ call a function in a child component from its parent component

Well the other answers are just correct, but I think some times that function is supposed to be called with the flow of the data the angular way from parent to child, so what you actually need is to run a function every time a variable has changed in the parent component. see below:

@Component({
  selector: "my-app",
  templateUrl: "./app.component.html",
  styleUrls: ["./app.component.css"]
})
export class AppComponent {
  name = "Angular";
  variable = "yes!";
  toggle() {
    this.variable = this.variable === "yes!" ? "hell no!" : "yes!";
  }
}

app tempalte:

<button (click)="toggle()">Toggle</button>

Parent says: {{variable}}    

<p>
 <app-child [childVar]="variable"></app-child>
</p>

child component:

export class ChildComponent implements OnInit {
  _childVar: string; // if you need to record the value and access later in child component
  counter = 0;

  @Input()
  set childVar(value: string) {
    this._childVar = value;
    this.childFunction(); // the answer is here
  }

  childFunction() {
    this.counter++;
    console.log("called child function");
  }

}

test here https://stackblitz.com/edit/angular-1rywfc

For calling a function of a child, you'll need @ViewChild. However, for showing/hiding a component, you are better off solving this within the template:

<parent>
    <button (click)="showChild=!showChild">Toggle child</button>
    <child *ngIf="showChild"></child>
</parent>

No need for declaring a custom function hide().

Inside of your template, using template variables/references:

<parent (click)="yourChild.hide()">
    <child #yourChild></child>
</parent>

live-demo: https://stackblitz.com/edit/angular-so-3?file=src%2Fapp%2Fapp.component.html

OR

Inside of your component:

import { ..., ViewChild, ... } from '@angular/core';

// ...

export class ParentComponent {
   @ViewChild('yourChild' /* #name or Type*/, {static: false}) child;

   ngAfterViewInit() {
      console.log('only after THIS EVENT "child" is usable!!');
      this.child.hide();
   }
}

Inside of your component (option2):

import { ..., ViewChild, ... } from '@angular/core';
import { ..., ChildComponent, ... } from '....';

// ...

export class ParentComponent {
   @ViewChild(ChildComponent /* #name or Type*/, {static: false}) child;

   ngAfterViewInit() {
      console.log('only after THIS EVENT "child" is usable!!');
      this.child.hide();
   }
}

See the official docs: https://angular.io/docs/ts/latest/cookbook/component-communication.html#!#parent-to-view-child