F (x) = 1/x shifts up 12 units and right 7 units

What is the equation

F (x) = (1/x-7) + 12 because the graph goes seven unit right we need to use opposite sign so + 7 become - 7.

Do the right first. It's the one that you have to pay the most attention to because it is any intuative. y = 1 / (x - 7) That looks like it should shift to the left. But it does not. Take a simple example

if y = 1/x is used first then if x = 1 then y = 1/1 = 1

if y = 1 / (x - 7) is considered then if x = 1 then y = 1 / (1 - 7) = - 1/6

The question is where does 1/x = - 1/6 the answer is when x = - 6

So the same answer is obtained with a shift to the right. Try this a couple of times to convince yourself of it.

To shift the graph up, all you need do is add 12.

y = 1 / (x - 7) + 12 is your answer. I'll put a graph up to show you how it works.

Notice the blue function. It is shifted up 12 (which you can see from the portion that starts from the left and eventually heads down. And then it is also going right (same part of the blue graph.

The red graph is y = 1/x