Write a rule for the pattern below. Use $x$ to represent the step number (instead of $n$ ). Assume the first step is step 1.

Step 1 ：Observe the sequence: [1, 4, 9, 16, 25]

Step 2 ：Notice the differences between consecutive terms: [3, 5, 7, 9]

Step 3 ：The differences increase by 2 each time, indicating a quadratic function of the form \(ax^2 + bx + c\)

Step 4 ：Using the first three terms, find the coefficients a, b, and c

Step 5 ：The rule for the pattern is \(f(x) = x^2\)

Step 6 ：\(\boxed{f(x) = x^2}\)