$(function() {
    $('#category-1-button a').bind('click', function() {
        $(this).css({opacity:'1'});
        $('#category-2-button a,#category-3-button a').css({opacity:'0.4'});
        $('#blog-headers').css({backgroundPosition: '0 0'});
        $('#category_2,#category_3').hide(0, function() {
            $('#category_1').show(0);
        });
    });
});

$(function() {
    $('#category-2-button a').bind('click', function() {
        $(this).css({opacity:'1'});
        $('#category-1-button a,#category-3-button a').css({opacity:'0.4'});
        $('#blog-headers').css({backgroundPosition: '0 -144px'});
        $('#category_1,#category_3').hide(0, function() {
            $('#category_2').show(0);
        });
    });
});

$(function() {
    $('#category-3-button a').bind('click', function() {
        $(this).css({opacity:'1'});
        $('#category-1-button a,#category-2-button a').css({opacity:'0.4'});
        $('#blog-headers').css({backgroundPosition: '0 -288px'});
        $('#category_1,#category_2').hide(0, function() {
            $('#category_3').show(0);
        });
    });
});

$(function() {
    $('#category-1-button a, #category-2-button a, #category-3-button a').click(function () {
        $('#category-1-button a,#category-2-button a,#category-3-button a').not(this).css({opacity:'0.4'});
        $(this).css({opacity:'1'});
        var myParent = $(this).parent();
        if (myParent == $('#category-1-button')) {
            $('#blog-headers').css({backgroundPosition: '0 0'});
            $('#category_3,#category_2').hide(0, function() {
                $('#category_1').show(0);
            });
        } else if (myParent == $('#category-2-button')) {
            $('#blog-headers').css({backgroundPosition: '0 -144px'});
            $('#category_1,#category_3').hide(0, function() {
                $('#category_2').show(0);
            });
        } else if (myParent == $('#category-3-button')) {
            $('#blog-headers').css({backgroundPosition: '0 -288px'});
            $('#category_1,#category_2').hide(0, function() {
                $('#category_3').show(0);
            });
        }
    });
}

$(function() {
    var categories = $('[id^="category_"]');
    var category_buttons_a = $('.category_button a').each(function( idx ) {
        $(this).bind('click', function() {
            $(this).css({opacity:'1'});
            category_buttons_a.not(this).css({opacity:'0.4'});
            $('#blog-headers').css({backgroundPosition: '0 ' + (idx * -144) + 'px'});
            categories.hide().filter( '#category_' + (idx + 1) ).show();
        });
    });
});

(function($){
"use strict";
var $categoryButtonLinks;

$categoryButtonLinks = $('#category-1-button a, #category-2-button a, #category-3-button a').click(clickCategoryButtonLink);

$categories = $('#category_1, #category_2, #category_3');

function clickCategoryButtonLink(e)
{
  var $this, $category, index, offset;
  $this = $(this).css('opacity', '1');
  index = $categoryButtonLinks.index($this);
  offset = -144 * index;
  index += 1;
  $category = $('#category_'+index);
  $categoryButtonLinks.not($this).css('opacity', '0.4');
  $('#blog-headers').css('background-position', '0 ' + offset + 'px' );
  $categories.not($category).hide(0, function(){
    $category.show(0);
  });
}

})(jQuery);

<div id="class="category-1-button" class="category_button">
  <a href="#Category_1">Category 1</a>
</div>

.category_button a {
  opacity: 0.4;
}

.category {
   display: none;
 }

/* The following rules/selectors could/should be generated by a script */
.category_1_selected #category-1-button a,
.category_2_selected #category-2-button a,
.category_3_selected #category-3-button a {
  opacity: 1;
}

.category_1_selected #category_1,
.category_2_selected #category_2,
.category_3_selected #category_3 {
  display: block;
}

.category_1_selected #blog-headers {
   background-position: 0 0;
 }

.category_2_selected #blog-headers {
   background-position: 0 -144px;
 }

.category_3_selected #blog-headers {
   background-position: 0 -288px;
 }

$(function() {
  var category_buttons_a = $('.category_button a').click(function() {
    // I'm putting the class on the body as an example, but any other element the
    // surrounds the buttons, categorys and the blog header is fine.
    $("body").removeClass().addClass(this.href.slice(1) + "_selected");
  });
});

<div>
  <a href="#Category_1" id="class="category-1-button" class="category_button">Category 1</a>
</div>