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Sagot :
To determine the type of function represented by the given table, we'll analyze the relationship between the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values. Here is the table for reference:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & -7 & -2 & 3 & 8 & 13 & 18 \\ \hline \end{array} \][/tex]
### Step-by-Step Solution:
1. List the given [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -7 \\ 1 & -2 \\ 2 & 3 \\ 3 & 8 \\ 4 & 13 \\ 5 & 18 \\ \hline \end{array} \][/tex]
2. Calculate the differences between consecutive [tex]\( y \)[/tex]-values:
[tex]\[ \begin{array}{|c|c|c|} \hline x & y & \Delta y \\ \hline 0 & -7 & - \\ 1 & -2 & -2 - (-7) = 5 \\ 2 & 3 & 3 - (-2) = 5 \\ 3 & 8 & 8 - 3 = 5 \\ 4 & 13 & 13 - 8 = 5 \\ 5 & 18 & 18 - 13 = 5 \\ \hline \end{array} \][/tex]
So, the differences between consecutive [tex]\( y \)[/tex]-values are all 5.
3. Analyze the differences:
Since the differences between consecutive [tex]\( y \)[/tex]-values are constant (5), we have a consistent rate of change.
### Conclusion:
A function that has a constant rate of change in [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is a linear function.
Thus, the type of function represented by the table is linear.
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & -7 & -2 & 3 & 8 & 13 & 18 \\ \hline \end{array} \][/tex]
### Step-by-Step Solution:
1. List the given [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -7 \\ 1 & -2 \\ 2 & 3 \\ 3 & 8 \\ 4 & 13 \\ 5 & 18 \\ \hline \end{array} \][/tex]
2. Calculate the differences between consecutive [tex]\( y \)[/tex]-values:
[tex]\[ \begin{array}{|c|c|c|} \hline x & y & \Delta y \\ \hline 0 & -7 & - \\ 1 & -2 & -2 - (-7) = 5 \\ 2 & 3 & 3 - (-2) = 5 \\ 3 & 8 & 8 - 3 = 5 \\ 4 & 13 & 13 - 8 = 5 \\ 5 & 18 & 18 - 13 = 5 \\ \hline \end{array} \][/tex]
So, the differences between consecutive [tex]\( y \)[/tex]-values are all 5.
3. Analyze the differences:
Since the differences between consecutive [tex]\( y \)[/tex]-values are constant (5), we have a consistent rate of change.
### Conclusion:
A function that has a constant rate of change in [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is a linear function.
Thus, the type of function represented by the table is linear.
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