I would create a Jasmine fixture, and call the click event on that fixture. After this, you can make assertions about the state of the fixture.
I usually use a plugin called jasmine-jquery for this: https://github.com/velesin/jasmine-jquery
The code would end up looking something like this:
var fixture = setFixture("some_html");
fixture.find('.link_image').trigger('click'); //.find() accepts a JQuery selector
expect(fixture.find('#DIV_1').toBeHidden();
expect(fixture.find('#DIV_2').toBeVisible();
Also, if you template is another file (maybe loaded through AMD) use this function:
var fixture = loadFixture('path/to/amd/template');
I would strongly recommend using the the AMD method to load the same templates you use in production, otherwise you must re-create your HTML as fixtures for the tests and then at that point you are just testing your fixtures and not your actual code.