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

Explanation:

Step1: Recall absolute value property

For all real $x$, $|x+1| \geq 0$

Step2: Multiply by -2 (reverse inequality)

$-2|x+1| \leq -2 \times 0$
$\implies f(x) \leq 0$

Answer:

all real numbers less than or equal to 0