>>13228029This isn't complicated. Look, I'll explain it to you. You look at the functions as being pieced together via translation. For instance, we can see that from 0 to 2, the function is simply . Now, from 2 to 6, it gets more "complicated". It's basically the function , but shifted to the right by 4, so we'd say . Finally, from 6 to 9, we once again have the function, but shifted by 8 to the right, thus .
If we wish to combine this all into one expression, we can simply write:
Now, if you're familiar with absolute values, then you may also recognise the function within the graph, which will allow you to simplify the expression further. Namely, as the anon here
>>13227860 has pointed out, we can see that from 0 to 4, we have the function , but shifted to the right by 2 and upwards by 2, which gives us . Likewise, we recognise that from 4 to 9, it's simply the function , but shifted to the right by 6 and downwards by 2, which gives us .
Again, by combining it all into one expression, we obtain:
