Issue with URI rewrite

So when our users enter support.yourdomain.com it goes off to support.3rdpartywebsite.com I am assuming and want the end user to not know that support.3rdpartywebsite.com URL and hit it direct.

if you just want to change http host header in request only, you can use HTTP::header replace command but if support.3rdpartywebsite.com is also embedded in response body (so, you have to rewrite it back to support.yourdomain.com), you may need to use proxypass which Mark suggested.

e.g.

 config

root@(ve11c)(cfg-sync In Sync)(Active)(/Common)(tmos) list ltm virtual bar
ltm virtual bar {
    destination 172.28.24.10:80
    ip-protocol tcp
    mask 255.255.255.255
    pool foo
    profiles {
        http { }
        tcp { }
    }
    rules {
        qux
    }
    source 0.0.0.0/0
    source-address-translation {
        type automap
    }
    vs-index 19
}
root@(ve11c)(cfg-sync In Sync)(Active)(/Common)(tmos) list ltm pool foo
ltm pool foo {
    members {
        200.200.200.101:80 {
            address 200.200.200.101
        }
    }
}
root@(ve11c)(cfg-sync In Sync)(Active)(/Common)(tmos) list ltm rule qux
ltm rule qux {
    when HTTP_REQUEST {
  if { [HTTP::host] eq "support.yourdomain.com" } {
    HTTP::header replace Host "support.3rdpartywebsite.com"
  }
}
}

 trace

[root@ve11c:Active:In Sync] config  ssldump -Aed -nni 0.0 port 80
New TCP connection 1: 172.28.24.1(53863) <-> 172.28.24.10(80)
1427071308.3080 (0.0279)  C>S
---------------------------------------------------------------
GET /someting HTTP/1.1
User-Agent: curl/7.15.5 (i686-redhat-linux-gnu) libcurl/7.15.5 OpenSSL/0.9.8b zlib/1.2.3 libidn/0.6.5
Accept: */*
Host: support.yourdomain.com

---------------------------------------------------------------

New TCP connection 2: 200.200.200.14(53863) <-> 200.200.200.101(80)
1427071308.3122 (0.0030)  C>S
---------------------------------------------------------------
GET /someting HTTP/1.1
User-Agent: curl/7.15.5 (i686-redhat-linux-gnu) libcurl/7.15.5 OpenSSL/0.9.8b zlib/1.2.3 libidn/0.6.5
Accept: */*
Host: support.3rdpartywebsite.com

---------------------------------------------------------------