Respuesta :
Answer: Choice B
The set notation includes all values from -5 to 0, but the domain only includes the integer values
eg: something like -1.2 is in the second set, but it is not in the set {-5,-4,-3,-2,-1}
==========================================================
Further explanation:
Let's go through the answer choices one by one
- A. This is false because 0 does not come before -5, but instead -5 is listed first. The order -5,-4,-3,-2,-1,0 is correct meaning that [tex]-5 \le x \le 0[/tex] is the correct order as well.
- B. This is true. A value like x = -1.2 is in the set [tex]\left\{x| -5 \le x \le 0\right\}[/tex] since -1.2 is between -5 and 0; but -1.2 is not in the set {-5, -4, -3, -2, -1, 0}. So the distinction is that we're either considering integers only or all real numbers in this interval. To ensure that we only look at integers, the student would have to write [tex]\left\{x| x\in\mathbb{Z}, \ -5 \le x \le 0\right\}[/tex]. The portion [tex]x \in \mathbb{Z}[/tex] means "x is in the set of integers". The Z refers to the German word Zahlen, which translates to "numbers".
- C. This is false. The student used the correct inequality signs to indicate x is -5 or larger and also 0 or smaller; basically x is between -5 and 0 inclusive of both endpoints. The "or equal to" portions indicate we are keeping the endpoints and not excluding them.
- D. This is false. Writing [tex]-5 \ge x \ge 0[/tex] would not make any sense. This is because that compound inequality breaks down into [tex]-5 \ge x \ \text{ and } \ x \ge 0[/tex]. Try to think of a number that is both smaller than -5 AND also larger than 0. It can't be done. No such number exists.
