example of PanResponder(ES6 format) from http://browniefed.com/blog/react-native-animated-api-with-panresponder/

React-Native Animation & PanResponder

import React, { Component } from 'react';
import {
  AppRegistry,
  StyleSheet,
  View,
  Animated, 
  PanResponder
} from 'react-native';
const SQUARE_DIMENSIONS = 100;

export default class AnimatedFlick extends Component{
    constructor(){
        super();
        this.state = {
            pan: new Animated.ValueXY()
        };
    }
    
    componentWillMount(){
        this._animatedValueX = 0;
        this._animatedValueY = 0; 
        this.state.pan.x.addListener((value) => this._animatedValueX = value.value);
        this.state.pan.y.addListener((value) => this._animatedValueY = value.value);

        this._panResponder = PanResponder.create({
            onMoveShouldSetResponderCapture: () => true,
            onMoveShouldSetPanResponderCapture: () => true,
            onPanResponderGrant: (e, gestureState) => {
              this.state.pan.setOffset({x: this._animatedValueX, y: this._animatedValueY});
              this.state.pan.setValue({x: 0, y: 0});
            },
            onPanResponderMove: Animated.event([
                  null, {dx: this.state.pan.x, dy: this.state.pan.y},
            ]),
            onPanResponderRelease: () => {
              Animated.spring(this.state.pan, {
                toValue: 0
              }).start();
            }
        });
    }

    componentWillUnmount(){
        this.state.pan.x.removeAllListeners();  
        this.state.pan.y.removeAllListeners();
    }

    getStyle = () => {
        return [
            styles.square, 
            {
                transform: [
                    { translateX: this.state.pan.x },
                    { translateY: this.state.pan.y },
                    { rotate: this.state.pan.x.interpolate({
                        inputRange: [-200, 0, 200],
                        outputRange: ["-30deg", "0deg", "30deg"]
                        })
                    }
                ]
            },
            {
              opacity: this.state.pan.x.interpolate({
                  inputRange: [-200, 0, 200],
                  outputRange: [0.5, 1, 0.5]
                })
            }
        ];
    }

    render(){        
        return (
            <View style={styles.container}>
                <Animated.View 
                style={this.getStyle()} 
                {...this._panResponder.panHandlers}
                />
            </View>
        );
    }
}

const styles = StyleSheet.create({
    container: {
      flex: 1,
      alignItems: 'center',
      justifyContent: 'center'
    },
    square: {
      width: SQUARE_DIMENSIONS,
      height: SQUARE_DIMENSIONS,
      backgroundColor: 'blue'
    } 
});