Question

at which x-values are the output values of the floor function $g(x) = \lfloor x \
floor$ and the ceiling function $h(x) = \lceil x \
ceil$ equal? check all that apply. \
$\square$ $-8$ \
$\square$ $-5.2$ \
$\square$ $-1.7$ \
$\square$ $0$ \
$\square$ $2.4$

Explanation:

Step1: Recall floor and ceiling definitions

The floor function $\lfloor x
floor$ gives the greatest integer less than or equal to $x$. The ceiling function $\lceil x
ceil$ gives the least integer greater than or equal to $x$. For $\lfloor x
floor=\lceil x
ceil$, $x$ must be an integer (since for non - integers, $\lfloor x
floor < \lceil x
ceil$).

Step2: Check each value

• For $x = - 8$: $\lfloor - 8

floor=-8$ and $\lceil - 8
ceil=-8$. So they are equal.

• For $x=-5.2$: $\lfloor - 5.2

floor=-6$ and $\lceil - 5.2
ceil=-5$. Not equal.

• For $x = - 1.7$: $\lfloor - 1.7

floor=-2$ and $\lceil - 1.7
ceil=-1$. Not equal.

• For $x = 0$: $\lfloor 0

floor = 0$ and $\lceil 0
ceil=0$. Equal.

• For $x = 2.4$: $\lfloor 2.4

floor=2$ and $\lceil 2.4
ceil=3$. Not equal.

Answer:

-8, 0 (the checkboxes for -8 and 0 should be selected)