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1 month ago

What is the domain of the function shown in the table

Mathematics

2 answers:

Leona [12.6K]1 month ago

8 0

The appropriate choice is $\boxed{\bf option\ B}$ , meaning that the function's domain is $\boxed{(-2,-1,0,1)}$ .

Further details:

In this case, the function is presented as a collection of ordered pairs detailed in Table 1 (included at the end).

The function can generally be expressed as $\{(x,y)|x,y\in\mathbb{R} \}$ , with $x$ representing the domain of the function, $y$ being the range and $\mathbb{R}$ indicating the set of real numbers.

The domain consists of all points where the function is defined, which includes all potential values of $x$ that yield an output $y$ .

The range refers to all output values of $y$ derived from the specified domain. $x$

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

For different values of $f(x)$ , the corresponding outcomes for $x$ can be expressed as follows:

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

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

Option (A)

In this scenario, the domain is $(-2,0),(-1,1),(0,2),(1,3)$ .

The provided domain is represented in function form where $x$ (domain) corresponds to $-2,-1,0,1$ and $y$ (range) represents $0,1,2,3$ .

Thus, this representation does not accurately reflect the domain.

The representation corresponds to the ordered pairs that define a function.

Therefore, the option (A) is incorrect.

Option (B)

In this case, the domain is $(-2,1,0,1)$ .

Here, the domain of the function $\{(-2,0),(-1,1),(0,2),(1,3)\}$ matches $(-2,1,0,1)$ , which coincides with choice (B).

Thus, the option (B) is correct.

Option (C)

In this example, the domain is $(0,1,2,3)$ .

And the function's domain $\{(-2,0),(-1,1),(0,2),(1,3)\}$ does not align with the choice (C).

Therefore, the option (C) is incorrect.

Option (D)

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

The function's domain $\{(-2,0),(-1,1),(0,2),(1,3)\}$ does not correspond with option (D).

Thus, the option (D) is incorrect.

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

Hence, the option (B) is correct.

Learn more

1. Problem regarding the range of the function .

2. Problem concerning the domain of the function .

3. Issue related to domain and range of the function .

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.

PIT_PIT [12.4K]1 month ago

4 0

we know that

The function's domain consists of the x values for which the function is valid, while the range encompasses the values produced by the function

in this problem

The values for the function's domain are $(-2,-1,0,1)$

The corresponding values for the function's range are $(0,1,2,3)$

therefore

the selected response is option B

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

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