a step function ( h(x) ) is represented by ( y = -2x ). which phrase best describes the range of the…

Explanation:

Step1: Recall the definition of the greatest - integer function

The greatest - integer function (y = [x]) gives the greatest integer less than or equal to (x). The output of (y=[x]) is an integer. Let (n=[x]), where (n\in\mathbb{Z}) (the set of integers).

Step2: Analyze the function (y = - 2[x])

If (n = [x]) and (y=-2[x]), then (y=-2n). Since (n) is an integer, when (n = 0), (y = 0); when (n=1), (y=-2); when (n = - 1), (y = 2); when (n = 2), (y=-4); when (n=-2), (y = 4) and so on.

Step3: Check the range of the function

The set of all values of (y=-2[x]) is of the form (y = 2k), where (k\in\mathbb{Z}). The set of all real numbers includes non - integer values, and the function (y=-2[x]) does not take non - integer values. The set of all rational numbers also includes non - integer values. The set of all negative integers does not include non - negative even integers (e.g., when (n = 0), (y = 0); when (n=-1), (y = 2)).

Answer:

all even integers