Rates of Change

If the rate of change of f is positive the graph of f is…

increasing

If the rate of change of f is negative the graph of f is…

decreasing

If the rate of change of f is increasing the graph of f is…

concave up

If the rate of change of f is decreasing the graph of f is…

concave down

If the rate of change is positive this means that… (how do the inputs and outputs vary?)

as one value increases or decreases, the other value does the same.

If the rate of change is negative this means that… (how do the inputs and outputs vary?)

as one value increases, the other value decreases in quantity and vice versa

A linear functions average rate of change, changes at a rate of…

ZERO

A quadratic functions rate of change is changing at a…

constant rate (the rate of change over consecutive equal-length input-value intervals is linear.)

talking about the intervals (aroc or roc)

RATE OF CHANGE (increasing/decreasing/constant) (positive/negative/zero)

talking about concavity (aroc or roc)

AVERAGE RATE OF CHANGE

Average rate of change is increasing…

concave up

Average rate of change is decreasing…

concave down

RATE OF CHANGE OF F descriptors (study 1.2b notes)

positive, negative, increasing, decreasing

GRAPH OF F descriptors (study 1.2b notes)

increasing, decreasing, concave up, concave down