Identifying Linear Functions & Function Notation

A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Function notation is a way to represent functions in mathematics. It uses symbols like f(x) to denote the output of a function f for a given input x.

A linear function can be identified if the points form a straight line when plotted on a graph.

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the function f(x) = mx + b.

f(0) = 2(0) + 3 = 3.

Linear functions graph to straight lines, while nonlinear functions graph to curves or other shapes.

A table represents a linear function if the differences between consecutive y-values are constant for equal differences in x-values.

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

The slope of the function f(x) = -x + 5 is -1.