Does the table represent a function?

$x$ 0 1 2 2 3 4

$f(x)$ -5 -2 0 2 4 7

Ayes
Bno
Cundefined
Dnot enough information

Question

03-11-2026
Mathematics

Answered

Does the table represent a function?

$x$ 0 1 2 2 3 4

$f(x)$ -5 -2 0 2 4 7

Ayes
Bno
Cundefined
Dnot enough information

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T21:07:02-05:00

A relation is a function only if each input maps to exactly one output.
In the provided table, the input $x=2$ is associated with two different outputs: $0$ and $2$.
Because a single input maps to multiple outputs, the relation is not a function.
The correct option is $\boxed{b}$.

Explanation

Analyzing the Definition of a Function

A relation is defined as a function if each input (the $x$-value) corresponds to exactly one output (the $f(x)$-value). To determine if the given table represents a function, we must examine the input $x$-values and ensure that no single $x$-value is mapped to more than one distinct $f(x)$-value. The table provided is as follows:
\[ @@TABLE_TOKEN_0@@ \]

Evaluating the Table Data

By examining the table, we identify the domain of the relation as $\{0, 1, 2, 3, 4\}$. We check the mapping for each input value:

For $x=0$, $f(0) = -5$
For $x=1$, $f(1) = -2$
For $x=2$, we see two entries: one where $f(2) = 0$ and another where $f(2) = 2$
For $x=3$, $f(3) = 4$
For $x=4$, $f(4) = 7$

The input $x=2$ is associated with two different outputs, $0$ and $2$. Since a function must assign exactly one unique output value for every input in its domain, the presence of multiple outputs for a single input confirms that this relationship fails the vertical line test and the formal definition of a function.

Conclusion

Based on the analysis, the relation is not a function because the input $x=2$ corresponds to two distinct values, $0$ and $2$. Therefore, the correct answer is b. no. The final result is $\boxed{b}$.

Examples

Imagine you are looking at a vending machine menu where each button represents an input (x). If pressing a single button, like button 'A2', sometimes dispensed a soda and other times dispensed a candy bar, you would be very confused because there is no consistency. Just like that, a mathematical function must be predictable—every input must lead to exactly one specific output. In data sets, identifying these inconsistencies is vital for ensuring your models, schedules, or algorithms work reliably.

Does the table represent a function? $x$012234 $f(x)$-5-20247 AyesBnoCundefinedDnot enough information

Verified Answer :

Explanation

Examples

Related Questions

Does the table represent a function?

$x$ 0 1 2 2 3 4

$f(x)$ -5 -2 0 2 4 7

Ayes
Bno
Cundefined
Dnot enough information