Question

Fill in the question mark in the table

x f(x)
-2 1
-1 -2
0 -3
1 ?

Answer 1

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 \( f(x) \):

1. From \( f(-2) \) to \( f(-1) \): \( 1 \) to \( -2 \) (a decrease of \( 3 \))
2. 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 \(-4\).