How do I preform this equation

Question

Write an equation of the function   that is the graph of   , but shifted left 2 units and shifted down 2 units.

Answer 1

The transformations of a function f(x) into g(x) are:

g(x) = a·f(b(x-c)) + d

1. a = vertical stretch
2. b = horizontal stretch (=1/b)
3. c = horizontal shift
4. d = vertical shift

In your problem, f(x) = |x|, and a = 1 (no vertical stretch), b = 1 (no horizontal stretch), c = -2 (shift left 2 units), and d = -2 (down two units).

g(x) = 1·|1(x-(-2)| - 2 = |x+2| - 2