Question

A step function h(x) is represented by y = –2⌊x⌋. Which phrase best describes the range of the function h(x)?

Answer 1

The value of step function is an integer number from negative infinity to positive infinity. So the phrase is "all the integer numbers, Z".

Answer 2

The range of the function h(x) is all even integers.

Explanation:

Range is the set of outputs and y values.

It is given that the function h(x) is represented by y = –2⌊x⌋.

Here, ⌊x⌋ represent the greatest integer function.

The greatest integers function is

`f(x)=\begin{cases}-1 & \text{ if } -1\leq x<0 \\ 0 & \text{ if } 0\leq x<1 \\1 & \text{ if } 1\leq x<2\\... & \text{ if } ... \\n & \text{ if } n\leq x<n+1 \end{cases}`

Range of a greatest integer function is all integers.

The function is 2 times of greatest integer function.

`h(x)=\begin{cases}2(-1) & \text{ if } -1\leq x<0 \\ 2(0) & \text{ if } 0\leq x<1 \\2(1) & \text{ if } 1\leq x<2\\... & \text{ if } ... \\2(n) & \text{ if } n\leq x<n+1 \end{cases}`

Therefore the range of h(x) is all even integers.