Answer:
The range of the function h(x) is all even integers.
Step-by-step 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
[tex]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}[/tex]
Range of a greatest integer function is all integers.
The function is 2 times of greatest integer function.
[tex]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}[/tex]
Therefore the range of h(x) is all even integers.
