Given the tables of input [tex]$x$[/tex] and output [tex]$y$[/tex] values, determine whether the tables represent a function.
Table 1:
[tex]\begin{tabular}{|l|l|l|l|l|l|}
\hline $x$ & 1 & 2 & 3 & 4 & 5 \\
\hline $y$ & 8 & 11 & 16 & 23 & 32 \\
\hline \end{tabular}[/tex]
A. Yes
B. No
Table 2:
[tex]\begin{tabular}{|l|l|l|l|l|l|l|}
\hline $x$ & -5 & -5 & -1 & 4 & 6 & 10 \\
\hline $y$ & 20 & 12 & 0 & 20 & 42 & 110 \\
\hline \end{tabular}[/tex]
A. Yes
B. No
Answer (2)
Table 1 represents a function because each x value has only one y value.
Table 2 does not represent a function because the x value -5 has two different y values.
Therefore, the answers are Yes for Table 1 and No for Table 2.
Explanation
Understanding the Problem We are given two tables of x and y values and asked to determine whether each table represents a function. A table represents a function if each x value has only one corresponding y value.
Analyzing Table 1 For Table 1, the x values are 1, 2, 3, 4, and 5. The corresponding y values are 8, 11, 16, 23, and 32. Each x value has only one y value. Therefore, Table 1 represents a function.
Analyzing Table 2 For Table 2, the x values are -5, -5, -1, 4, 6, and 10. The corresponding y values are 20, 12, 0, 20, 42, and 110. The x value -5 has two corresponding y values, 20 and 12. Therefore, Table 2 does not represent a function.
Conclusion Table 1 represents a function, so the answer is Yes. Table 2 does not represent a function, so the answer is No.
Examples
Imagine you are tracking the growth of a plant each day. If each day (x) has only one corresponding height (y), then the data represents a function. However, if on one day (x), you somehow recorded two different heights (y), then the data would not represent a function. Understanding functions helps us model real-world relationships where each input has a unique output.
Table 1 represents a function because each x value has a unique y value. Table 2 does not represent a function because the x value -5 has two different y values. Thus, the answers are Yes for Table 1 and No for Table 2.
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