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Let's analyze the data provided in the table to determine whether the relationship between \(x\) and \(y\) is linear, quadratic, or exponential.

### Data:
\[
\begin{array}{c|c}
x & y \\
\hline
-1 & 1 \\
0 & 0 \\
1 & 1 \\
2 & 4 \\
\end{array}
\]

#### 1. Linear Relationship
A linear relationship has the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. For a linear function, the change in \(y\) for a unit change in \(x\) should be constant.

Let's check the differences between consecutive \(y\) values:
- From \(y(0) - y(-1) = 0 - 1 = -1\

Learn how to determine if a relationship between x and y is linear, quadratic, or exponential using provided data and mathematical analysis. This problem explores key algebraic concepts and functions, suitable for high school students.

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