Module 4 - Glossary


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Module 4 - Rates of Change
Glossary of Terms

Approximation - A value that is nearly, but not exactly, correct. Numerical approximations often result from using a small number of significant digits. Approximation also refers to using a simpler model of a process, to make predictions easier.
Average Rate of Change - The ratio of the difference in a dependent variable with respect to an independent variable. For example, if the distance traveled is a function of time, then the ratio

(d₂-d₁) / (t₂-t₁)
is the average velocity (total distance divided by total time).
Continuous - Intuitively, a continuous function of one variable is a function who graph is connected, that is with no "holes" or "jumps".
Derivative - The instantaneous rate of change of a function at a point.
Instantaneous Rate of Change - The rate of change which would result if the time interval could be reduced to zero length. It is the limiting value of the average rate of change.
Secant Line - A line passing through two distinct points on a curve, usually the graph of a function.
Slope - The ratio of the difference in the dependent variable to the difference in the independent variable. For example, if y is a function of x, then the slope is given by

(y₂-y₁) / (x₂-x₁)
Tangent Line - A line whose slope is the same as the limiting value of the secant.