Question

Write a function rule for the table.

x ƒ(x)
–1 0
0 1
1 2
2 3


ƒ(x) = x + 1


ƒ(x) = x – 1


ƒ(x) = x


ƒ(x) = –1 – x

Answer 1

To find the function rule for the provided table values, we can examine the input-output pairs:

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

By observing the output values for each corresponding input value of \(x\), we can deduce a pattern:

- When \(x = -1\), \(f(x) = 0\)
- When \(x = 0\), \(f(x) = 1\)
- When \(x = 1\), \(f(x) = 2\)
- When \(x = 2\), \(f(x) = 3\)

It appears that as \(x\) increases by 1, \(f(x)\) also increases by 1. Therefore, we can hypothesize that the function adds 1 to the value of \(x\).

This can be expressed with the function rule:

\[
f(x) = x + 1
\]

Therefore, the correct function rule from the choices provided is:

\[
\boxed{f(x) = x + 1}
\]