The correct option is [tex]\boxed{\bf option\ B}[/tex] i.e., the domain of the function is [tex]\boxed{(-2,-1,0,1)}[/tex].
Further explanation:
Here, the function is given by the set of ordered pairs as shown in Table 1 (attached in the end).
The general form of the function is [tex]\{(x,y)|x,y\in\mathbb{R} \}[/tex], where [tex]x[/tex] is domain of the function, [tex]y[/tex] is the range of the function and [tex]\mathbb{R}[/tex] denotes the set of real numbers.
The domain of a function is the set of all those points where the function is defined that is all the possible values of [tex]x[/tex] such that the function gives the output [tex]y[/tex].
The range of the function is defined as all the values of [tex]y[/tex] when [tex]x[/tex] (domain) is defined.
The function is [tex]\{(-2,0),(-1,1),(0,2),(1,3)\}[/tex].
The value of [tex]f(x)[/tex] for different values of [tex]x[/tex] can be written as follows:
[tex]f(-2)=0,f(-1)=1,f(0)=2\text{ and }f(1)=3[/tex]
Therefore, the domain of the function is [tex](-2,-1,0,1)[/tex].
Option (A)
Here, the domain is [tex](-2,0),(-1,1),(0,2),(1,3)[/tex].
The given domain is in the function form where [tex]x[/tex] (domain) is [tex]-2,-1,0,1[/tex] and [tex]y[/tex] (range) is [tex]0,1,2,3[/tex].
Therefore, given represntation is not the correct representation of domain.
The given representation corresponds to the ordered pairs which defines a function.
Thus, the option (A) is incorrect.
Option (B)
Here, the domain is [tex](-2,1,0,1)[/tex].
And the domain of the function [tex]\{(-2,0),(-1,1),(0,2),(1,3)\}[/tex] is [tex](-2,1,0,1)[/tex] which is same as the option (B).
Thus, the option (B) is correct.
Option (C)
Here, the domain is [tex](0,1,2,3)[/tex].
And the domain of the function [tex]\{(-2,0),(-1,1),(0,2),(1,3)\}[/tex] is [tex](-2,1,0,1)[/tex] which is not same as the option (C).
Thus, the option (C) is incorrect.
Option (D)
Here, the domain is [tex](-2,-1,0,1,2,3)[/tex].
And the domain of the function [tex]\{(-2,0),(-1,1),(0,2),(1,3)\}[/tex] is [tex](-2,1,0,1)[/tex] which is not same as the option (D).
Thus, the option (D) is incorrect.
The domain of the function is [tex]\boxed{\bf (-2,1,0,1)}[/tex].
Therefore, the option (B) is correct.
Learn more
1. Problem on range of the function https://brainly.com/question/1435353.
2. Problem on domain of the function https://brainly.com/question/3852778.
3. Problem on domain and range of the function https://brainly.com/question/3412497.
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Relation and Function
Keywords: Function, range, domain, relation, ordered pairs, sets, real numbers, ordinates, abscissa, co-domain, interval , open interval, closed intervals, semi-closed intervals, semi-open intervals.
