Question

The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

(–∞, –7)
(–∞, –1)
(–∞, 1)
(–∞, 7)

Answer 1

g(x)=|x+1|-7 is |x| shifted left 1 (vertex at x = -1). The left branch decreases for x < -1, so the interval is (−∞, −1).