CFU Rules and Definitions

Vocabulary flashcards covering key terms from Unit 1: Function concepts, increasing/decreasing, concavity, and rate-of-change.

Function

A relation where each input x maps to exactly one output f(x).

Not a Function

A relation where an input x maps to more than one output.

Increasing Function

As x increases, f(x) increases (function value rises) for all x in its domain.

Decreasing Function

As x increases, f(x) decreases (function value falls) for all x in its domain.

Constant Function

f(x) is the same for every x in the domain; output does not change with input.

Average Rate of Change (AROC)

The average slope of the function over an interval [a, b], given by (f(b) - f(a)) / (b - a).

Slope of a Secant Line

The slope of the line through points (a, f(a)) and (b, f(b)).

Concave Up

The graph opens upward (cup-shaped). The average rate of change is increasing on the interval.

Concave Down

The graph opens downward (frown-shaped). The average rate of change is decreasing on the interval.

Point of Inflection

A point where the function changes concavity from concave up to concave down or vice versa.

Even Function

A function with symmetry about the y-axis: f(-x) = f(x).

Odd Function

A function with symmetry about the origin: f(-x) = -f(x).

Piecewise-Defined Function

A function defined by different expressions on different intervals of its domain.

Positive Function

f(x) > 0 for all x in the domain (the graph lies above the x-axis).

Negative Function

f(x) < 0 for all x in the domain (the graph lies below the x-axis).