A function is a mathematical relationship where each input produces exactly one output. We write f(x) = 2x + 3 to define a function. If x = 4, then f(4) = 2(4) + 3 = 11.

Linear functions produce straight lines when graphed. The equation y = mx + b is called slope-intercept form. The slope (m) describes how steep the line is, and the y-intercept (b) tells where the line crosses the y-axis.

To find slope between two points (x₁, y₁) and (x₂, y₂), use m = (y₂ − y₁)/(x₂ − x₁). A positive slope means the line rises from left to right. A negative slope means it falls. A slope of zero is a horizontal line.

The domain is all valid inputs, and the range is all valid outputs. For most linear functions, both the domain and range include all real numbers.