You're
stating transformations, so you don't necessarily have to do this with the given equation. All you have to know is what changes f(x) to what the question wants you to end up. In this case, you want g(x), which is g(x) = f(x+2) + 4 .
Let's take a look at what you need to do in order to change f(x) to f(x+2) + 4. I'll give you a hint: you'll have two steps. Why? Because you have two big differences from f(x) --> f(x+2) + 4
Step 1
Let's start off by doing the stuff in the brackets, because they're usually harder to change later.
Note: there's a general rule of thumb out there that states that you should do dilations, reflections and transformations respectively. Caveat here -this doesn't work for everything and as long as you state the steps in an order that receives the same graph, it doesn't matter which order you do them in.
Since there are no coefficients, there are no dilations involved. There are no reflections either, because the f(x) would have had negative coefficients. This means we have two translations.
To move something in the brackets, in terms of translations, we usually need to think a little backwards. A positive term gives a left shift in the x-axis, whilst a negative term gives shift to the right. (You can graph x2 and (x+1)2 to prove this yourself.)
The "+ 2" in the brackets therefore moves f(x) left 2 units. State this as "translate 2 units to the left" or similar.
Step 2
Now that we have gone from f(x) to f(x+2), we need to add the 4. This is a shift in the y-axis and is more instinctive. Positive units means a shift up and negative does the opposite.
Therefore, to go from f(x+2) to f(x+2)+4, we need to "translate 4 units up".
That's it! You transformed f(x) --> f(x+2) --> f(x+2)+4 .