Question

How do you identify the transformation of `h(x)=abs(x+3)-5`?

Answer 1

The graph of `f(x)=|x|` is shifted 3 units to the left and 5 units down.

Explanation:

Transformations of the `g(x)=f(x-c)` are horizontal shifts of `c`-units. The negative sign in there is particularly important. I usually find the shift by setting `x-c=0` and then solving. In this case `x+3=0\rightarrow x=-3`, so the graph is shifted 3 to the left (because of the negative sign).

Transformations of the form `g(x)=f(x)+d` are vertical shifts. In this case the shift goes exactly how you'd expect, with a positive value being a shift up and a negative value being a shift down, so the `-5` means a shift of 5 units down.