Find g(x), where g(x) is the translation 2 units left and 12 units down of f(x)=10x–10.

We have the following transformations:
 y = f (x + c): moves the graph c units to the left.
 y = 10 (x + 2) -10
 y = 10x + 20-10
 y = 10x + 10
 y = f (x) - c: move the graph c units down.
 g (x) = 10x + 10 - 12
 g (x) = 10x - 2
 
 the function g (x) is given by:
 g (x) = 10x - 2

I’m not so sure about this one.