Question
On your test you will be graded on your short response using the following rubric:
• The answer is correct. The student made no errors while solving.
• The answer shows that the student used problem-solving skills and reasoning.
• All work is shown or explained.
Describe the meaning of the word function in math. Consider the table below. Why does this table show a function?
x
-2
-2
-1
0
6
1
10
14
• The answer is correct. The student made no errors while solving.
• The answer shows that the student used problem-solving skills and reasoning.
• All work is shown or explained.
Describe the meaning of the word function in math. Consider the table below. Why does this table show a function?
x
-2
-2
-1
0
6
1
10
14
Answers
GPT-4o mini
In mathematics, a function is a specific relation between a set of inputs (called the domain) and a set of possible outputs (called the range), where each input is associated with exactly one output. This means that for every x-value (input), there is only one corresponding y-value (output).
To analyze the provided table:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 0 \\
-2 & 6 \\
-1 & 1 \\
10 & 14 \\
\hline
\end{array}
\]
We can see that there are two instances where the input \( x = -2 \) is associated with different outputs (\( y = 0 \) and \( y = 6 \)). This violates the definition of a function, because each input must correspond to only one output.
Thus, the table does not represent a function.
If we were to rewrite the table to ensure that each x-value corresponds to only one y-value, it would follow the criteria for a function. For example, if we had:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 0 \\
-1 & 1 \\
0 & 10 \\
6 & 14 \\
\hline
\end{array}
\]
In this case, each x-value has only one unique y-value, which confirms that it is a function.
To analyze the provided table:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 0 \\
-2 & 6 \\
-1 & 1 \\
10 & 14 \\
\hline
\end{array}
\]
We can see that there are two instances where the input \( x = -2 \) is associated with different outputs (\( y = 0 \) and \( y = 6 \)). This violates the definition of a function, because each input must correspond to only one output.
Thus, the table does not represent a function.
If we were to rewrite the table to ensure that each x-value corresponds to only one y-value, it would follow the criteria for a function. For example, if we had:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 0 \\
-1 & 1 \\
0 & 10 \\
6 & 14 \\
\hline
\end{array}
\]
In this case, each x-value has only one unique y-value, which confirms that it is a function.