To determine the function \( f(x) \) based on the table provided, we can analyze the relationship between the values of \( x \) and \( y \).
The table provides the following values:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 0 & -10 \ 1 & -9 \ 2 & -8 \ 3 & -7 \ \hline \end{array} \]
From the table, we can observe that as \( x \) increases by 1, \( y \) increases by 1 as well. This implies a linear relationship.
To find the function in the form \( f(x) = x + b \), we can determine the value of \( b \) by using one of the points from the table. Let's use the first point \((0, -10)\):
When \( x = 0 \): \[ f(0) = 0 + b = -10 \]
Solving for \( b \): \[ b = -10 \]
Thus, the function based on the relationship observed in the table can be expressed as:
\[ f(x) = x - 10 \]
Therefore, the answer is: \[ f(x) = x - 10 \]
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