automatic zoom to layer in arcgis js api

I'm trying to zoom to layer automatically as soon as the map finishes loading using the guide here. To be clear, I'm only loading one layer and just want to zoom in on one of the layers provided by the service.

js script

dojo.require("dijit.layout.BorderContainer");
dojo.require("dijit.layout.ContentPane");
dojo.require("esri.map");
dojo.require("esri.renderer");

dojo.require("esri.graphic");
dojo.require("esri.dijit.Legend");
dojo.require("esri.utils");

dojo.require("dijit.layout.AccordionContainer");
dojo.require("esri.layers.FeatureLayer");

var map;
var basemap;
var trafficmap;

var basemapServiceSource;
var featuremapServiceSource;
var trafficServiceSource;
var renderer;
var loading;

function init() {

    // for now, these are referring to a single source
    basemapServiceSource = "http://co-gis-01/ArcGIS/rest/services/dev_RTIA/rtia/MapServer";


    //Add the topographic layer to the map. View the ArcGIS Online site for services http://arcgisonline/home/search.html?t=content&f=typekeywords:service          
    basemap = new esri.layers.ArcGISDynamicMapServiceLayer(basemapServiceSource);
    basemap.setVisibleLayers([0, 1, 2, 4, 5, 6]);

    map = new esri.Map("map", {

            // remove logo
            logo:false
        });


    //loading image. id
    loading = dojo.byId("loadingImg");
    dojo.connect(map,"onUpdateStart",showLoading);
    dojo.connect(map,"onUpdateEnd",hideLoading);

    /*
        IDs of Layers for http://co-gis-01/ArcGIS/rest/services/dev_ExIS/exis/MapServer
            Site Name (0)
            Section ID (1)

            AADT some (2)
            AADT all (3)
            AdministrativeAreas_CongressionalDistricts (4)
            AdministrativeAreas_Provinces (5)
            AdministrativeAreas_Regions (6)
    */
    map.addLayer(basemap);

    // executes function on onLoad event
    dojo.connect(map, 'onLoad', function(theMap) { 


        dojo.connect(dijit.byId('map'), 'resize', map,map.resize);
        zoomToLayer();
    });
}


function zoomToLayer() {

    var requestHandle = esri.request({

        url: "http://co-gis-01/ArcGIS/rest/services/dev_RTIA/rtia/MapServer/2",
        content: { f:"json" },
        callbackParamName: "callback"
    });

    requestHandle.then(requestSucceeded, requestFailed);
}

function requestSucceeded(response, io) {


    var extent = new esri.geometry.Extent(response.extent);
    dojo.byId("extent").innerHTML = dojo.toJson(extent.toJson());
    map.setExtent(extent);
}

function requestFailed()    {

    alert("requestFailed");
}


function showLoading()  {

    esri.show(loading);
    map.disableMapNavigation();
    map.hideZoomSlider();
}

function hideLoading(error) {

    esri.hide(loading);

    map.enableMapNavigation();
    map.showZoomSlider();       
}

dojo.addOnLoad(init);

html code










The problem is that the outputs of dojo.toJson(extent.toJson()) show the same extent, which is the full extent, no matter the layer. This particular layer that I would like to zoom to, http://co-gis-01/ArcGIS/rest/service...ia/MapServer/2, is just a filtered version of one of the "full-extent" layers. The filter is defined in the mapservice.

How do I correctly do this function?