ROC in Linear and Quadratic Functions Flashcards

Vocabulary flashcards covering the concepts of rates of change, first and second differences, and concavity used to identify linear and quadratic functions from tables of values.

Linear Function

A function where the average rate of change is constant for any two points, meaning equal changes in the input $x$ produce constant changes in the output $f(x)$.

Quadratic Function

A function whose first differences are not constant but whose second differences are constant, provided the input values change by a constant amount.

Average Rate of Change (AROC)

The ratio of the change in the output value to the change in the input value over a specific interval, calculated as $\frac{\Delta y}{\Delta x}$.

First Differences

The set of values found by calculating the change in the output values ($\Delta f(x)$) for consecutive input values when those inputs change by a constant amount.

Second Differences

The change in the first differences of a function; a constant value for these indicates a quadratic relationship.

Concave Up

A property of a function where the rate of change is increasing over an interval, which is indicated by positive second differences when the change in $x$ is constant.

Concave Down

A property of a function where the rate of change is decreasing over an interval, which is indicated by negative second differences when the change in $x$ is constant.

Neither (Linear or Quadratic)

A classification for functions whose average rate of change is not constant and whose second differences are also not constant.