Question

What is the domain of the function shown in the table

Answer 1

The correct option is $\boxed{\bf option\ B}$ i.e., the domain of the function is $\boxed{(-2,-1,0,1)}$.

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 $\{(x,y)|x,y\in\mathbb{R} \}$, where $x$ is domain of the function, $y$ is the range of the function and $\mathbb{R}$ 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 $x$ such that the function gives the output $y$.

The range of the function is defined as all the values of $y$ when $x$ (domain) is defined.

The function is $\{(-2,0),(-1,1),(0,2),(1,3)\}$.

The value of $f(x)$ for different values of $x$ can be written as follows:

$f(-2)=0,f(-1)=1,f(0)=2\text{ and }f(1)=3$

Therefore, the domain of the function is $(-2,-1,0,1)$.

Option (A)

Here, the domain is $(-2,0),(-1,1),(0,2),(1,3)$.

The given domain is in the function form where $x$ (domain) is $-2,-1,0,1$ and $y$ (range) is $0,1,2,3$.

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 $(-2,1,0,1)$.

And the domain of the function $\{(-2,0),(-1,1),(0,2),(1,3)\}$ is $(-2,1,0,1)$ which is same as the option (B).

Thus, the option (B) is correct.

Option (C)

Here, the domain is $(0,1,2,3)$.

And the domain of the function $\{(-2,0),(-1,1),(0,2),(1,3)\}$ is $(-2,1,0,1)$ which is not same as the option (C).

Thus, the option (C) is incorrect.

Option (D)

Here, the domain is $(-2,-1,0,1,2,3)$.

And the domain of the function $\{(-2,0),(-1,1),(0,2),(1,3)\}$ is $(-2,1,0,1)$ which is not same as the option (D).

Thus, the option (D) is incorrect.

The domain of the function is $\boxed{\bf (-2,1,0,1)}$.

Therefore, the option (B) is correct.

Learn more

1. Problem on range of the function brainly.com/question/1435353.

2. Problem on domain of the function brainly.com/question/3852778.

3. Problem on domain and range of the function 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.

Answer 2

we know that

The domain of the function are the values of x for which the function exists and the range of the function are the values of the function

in this problem

The domain of the function are the values $(-2,-1,0,1)$

The range of the function are the values $(0,1,2,3)$

therefore

the answer is the option B

$(-2,-1,0,1)$