Question

The absolute value function g(x) = |x + 7| − 4 is translated 5 units right and 2 units up to become g′(x). The quadratic function f(x), graphed below, is also moved 5 units right and 2 units up to become f′(x). Which of these two transformed functions has a range of y ≤ −2 and what is the vertex of this transformed function?
 g′(x) has a range of y ≤ −2 and its vertex is at (−2, −2).
 g′(x) has a range of y ≤ −2 and its vertex is at (2, −2).
 f′(x) has a range of y ≤ −2 and its vertex is at (3, −2).
 f′(x) has a range of y ≤ −2 and its vertex is at (−7, −6).

Answer 1

The correct answer is C. 

Answer 2

I think its C, if I'm being quite honest its kind of confusing for me too. Sorry