To find the value of \( f(1) \), we should look for a pattern in the given values of \( f(x) \).
Here are the values provided:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -2 & 1 \ -1 & -2 \ 0 & -3 \ 1 & ? \ \hline \end{array} \]
Let’s analyze the values of \( f(x) \):
- For \( x = -2 \), \( f(-2) = 1 \)
- For \( x = -1 \), \( f(-1) = -2 \)
- For \( x = 0 \), \( f(0) = -3 \)
The values of \( f(x) \) appear to follow a decreasing pattern. Let’s see the changes in \( f(x) \):
- From \( f(-2) \) to \( f(-1) \): \( 1 \) to \( -2 \) (a decrease of \( 3 \))
- From \( f(-1) \) to \( f(0) \): \( -2 \) to \( -3 \) (a decrease of \( 1 \))
If we observe the changes, they seem inconsistent, but we notice that it goes from positive at \( x = -2 \) to negative at \( x = -1 \) and \( x = 0 \).
Let’s look at a hypothesis based on the capacity to follow trends. We might check whether the function is linear or follows some polynomial form; however, to proceed without additional patterns we can guess the next logical value.
Checking between \( f(0) \) and \( f(1) \): If \( f(0) = -3 \), we might guess that \( f(1) \) = \( -4 \), continuing the downward trend.
Thus, let’s fill in \( f(1) \):
\[ f(1) = -4 \]
So the completed table would be:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -2 & 1 \ -1 & -2 \ 0 & -3 \ 1 & -4 \ \hline \end{array} \]
Thus, the answer for the question mark \( ? \) is \(-4\).