Question

What is the range of the function f(x) = –2|x + 1|?

all real numbers
all real numbers less than or equal to 0
all real numbers less than or equal to 1
all real numbers greater than or equal to 1

Answer 1

Since |x + 1| ≥ 0 for all x, −2|x + 1| ≤ 0. The maximum value 0 occurs at x = −1, and the expression decreases without bound as |x + 1| grows.

Range: all real numbers less than or equal to 0 (i.e. (−∞, 0]).