$('#selection').change(function() {
   var selected_value = $("input[name='kobegreat']:checked").val();

   $.ajax( {
       url: "kobegreat.php",
       data: {"name": selected_value},
       type: "GET",
       dataType: "json",

       success: function(json) {
           var $imgEl = $("img");
           if( $imgEl.length === 0) {
               $imgEl = $(document.createElement("img"));
               $imgEl.insertAfter('h3');
               $imgEl.attr("width", "300px");
               $imgEl.attr("alt", "kobepic");
           }
           var link = json.link + ".jpg";
           $imgEl.attr('src', link);
           alert("AJAX was a success");
      },
      cache: false
  });
});

<?php


   $db_user = 'test';
   $db_pass = 'test1';

   if($_SERVER['REQUEST_METHOD'] == "GET") {
       $value = filter_input(INPUT_GET, "name");
   }

   try {
       $conn = new PDO('mysql: host=localhost; dbname=kobe', $db_user, $db_pass);
       $conn->setAttribute(PDO:: ATTR_ERRMODE, PDO:: ERRMODE_EXCEPTION);
       $stmt = $conn->prepare('SELECT * FROM greatshots WHERE name = :name');
       do_search($stmt, $value);
  } catch (PDOException $e) {
      echo 'ERROR', $e->getMessage();
  }

  function do_search ($stmt, $name) {
      $stmt->execute(['name'=>$name]);

      if($row = $stmt->fetch()) {
          $return = $row;
          echo json_encode($return);
      } else {
          echo '<p>No match found</p>;
      }
  }

?>

<h2>Select a Great Kobe Moment.</h2>
<form id="selection" method="get">
   <input type="radio" name="kobegreat" value="kobe1" checked/>Kobe1
   <input type="radio" name="kobegreat" value="kobe2"/>Kobe2
   <input type="radio" name="kobegreat" value="kobe3"/>Kobe3
</form>

<div id="target">
    <h3>Great Kobe Moment!</h3>
</div>

greatshots(name, link)

name         link
------       --------
kobe1        images/kobe1
kobe2        images/kobe2
kobe3        images/kobe3