A function is a unique rule assigning output to each input. The function's graph shows these input-output pairs. We can compare two functions' characteristics, presented in various ways. For instance, we can compare the rate of change of a linear function illustrated in a value table and an algebraic formula.

The equation y = mx + b defines a straight-lined linear function, whereas non-linear functions, such as A = s2 (a function of a square's area in relation to its side length), do not follow this pattern. This function's graph doesn't form a straight line as shown by points (1,1), (2,4) and (3,9).

One can craft a function to model a linear relationship between two quantities. The function's rate of change and initial value can be established from a relationship description or two (x, y) values, derived from a graph or value table. The interpretation of the rate of change and initial value of a linear function can be derived from the situation it represents, its graph, or a table of values.

We can analyze the functional relationship between two quantities by examining a graph, such as understanding where the function increases or decreases, or determining its linearity.