Writing Functions

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

The slope of a line is a measure of its steepness, usually represented by 'm', calculated as the change in y divided by the change in x (rise/run).

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the slope-intercept form of a linear equation (y = mx + b).

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

A linear function is a function that graphs to a straight line, characterized by a constant rate of change (slope).

The independent variable is the input of a function (often x), while the dependent variable is the output (often y) that depends on the input.

The slope represents the rate of change; for example, in a cost function, it indicates how much the cost increases per unit.

A table of values lists pairs of input (x) and output (y) values that satisfy a function.

The x-intercept is the point where the line crosses the x-axis, indicating the value of x when y = 0.