Question

16.
Write a function rule for the table.

x ƒ(x)
–3 1
–2 2
–1 3
0 4

Answer 1

To find a function rule for the table, let's first observe the relationship between the input \( x \) and the output \( f(x) \).

The given values are:

\[
\begin{align*}
x & : -3, -2, -1, 0 \\
f(x) & : 1, 2, 3, 4 \\
\end{align*}
\]

We can notice the pattern of \( f(x) \) relative to \( x \):
- When \( x = -3, f(x) = 1 \)
- When \( x = -2, f(x) = 2 \)
- When \( x = -1, f(x) = 3 \)
- When \( x = 0, f(x) = 4 \)

It seems that the function \( f(x) \) increases by 1 as \( x \) increases by 1. Specifically, we can see that if we add 4 to \( x \), we obtain \( f(x) \):
- For \( x = -3 \): \( f(-3) = -3 + 4 = 1 \)
- For \( x = -2 \): \( f(-2) = -2 + 4 = 2 \)
- For \( x = -1 \): \( f(-1) = -1 + 4 = 3 \)
- For \( x = 0 \): \( f(0) = 0 + 4 = 4 \)

Based on this pattern, we can formulate the function rule:

\[
f(x) = x + 4
\]

Thus, the function rule for the table is:

\[
\boxed{f(x) = x + 4}
\]