MATHEMATICS HIGH SCHOOL

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

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Answer 1

Answer:

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

$f(x)=\begin{cases}-1 & \text{ if } -1\leq x<0 \n 0 & \text{ if } 0\leq x<1 \n1 & \text{ if } 1\leq x<2\n... & \text{ if } ... \nn & \text{ if } n\leq x<n+1 \end{cases}$

Range of a greatest integer function is all integers.

The function is 2 times of greatest integer function.

$h(x)=\begin{cases}2(-1) & \text{ if } -1\leq x<0 \n 2(0) & \text{ if } 0\leq x<1 \n2(1) & \text{ if } 1\leq x<2\n... & \text{ if } ... \n2(n) & \text{ if } n\leq x<n+1 \end{cases}$

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

Answer 2

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

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

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