"We live close to a freeway our pet couldn't possibly still be alive."
Not so, your pet may have made it across and is now scared and hiding once on the other side, be sure to continue your search for your lost pet.

"Our relatives live close by, our pet knows them, and will go there."
No so, often pets are more likely to be eating and hiding, needing help to be found.

"Our kitty is a mouser and he will be able to survive until he is found."
Not so, kitties that are lost feel preyed upon, leaving them to no longer hunt for mice in most cases.

"Many neighbors in our area feed strays and our pet will have something to eat while he is lost."
Not necessarily so. Your pet is the newby to the area and he will be lucky to get even one bite from any of those bowls left out, without having to fight for that one bite of food. He will eat "anything" while he is lost, from spiders to garbage not intended to eat, such as electrical tape that might have just a smattering of yesterday's food on it, left in an uncovered garbage can.

"My pet is so beautiful, I'm sure someone has found him and has made him theirs now."
Not always the case, don't depend on this kitties who are lost, eat and hide and are too frightened to go to someone unknown to them in most cases. He will be desperately waiting for you to find him. Dogs are often shooed and sent along their way.