Average rates and secant lines

Average rates of change and secant lines

Measure how a function changes over an interval using the change in output divided by the change in input. This precalculus practice set uses formulas, a synthetic data table and a coordinate graph to build reliable average-rate calculations. You will also write a secant-line equation through two points on a function.

Conceptual tasks distinguish an interval’s average rate from an endpoint value, a constant rate throughout the interval and a prediction made by the secant line. Applications examine output-per-input units, unequal time intervals, a missing endpoint value, a piecewise charge and the difference between average velocity and average speed.

Prerequisites

Review function evaluation, slope, point-slope equations and basic piecewise rules. Keep subtraction in a consistent order in the numerator and denominator, and verify that the input change is nonzero. All data are supplied; no regression tool or calculator is necessary.

Practice strategy

Find the two endpoint values before doing any division. Attach units to a contextual answer and check whether its sign matches the net change. Single-select and select-all items include worked explanations and checks. A negative or zero average summarizes the endpoints; further information is needed to describe every intermediate change.