AP Precalculus Topic 1.1 Change in Tandem - Vocabulary

Vocabulary flashcards covering key concepts from Topic 1.1 Change in Tandem notes.

Function

A relation that assigns to every input value in its domain exactly one output value in its range.

Domain

The set of all input values for which the function is defined.

Range

The set of all possible output values produced by the function.

Independent variable

The input variable (often x) whose values come from the domain.

Dependent variable

The output variable (often y) whose values form the range.

Each input has exactly one output

The defining criterion for a function: every input maps to a single output.

Vertical Line Test

A graphical test that checks whether a graph represents a function by seeing if any vertical line intersects the graph more than once.

Four representations

The four representations of a function: graphical, analytical (equations), numerical (tables), and verbal.

Graphical representation

A visual plot of the function on a coordinate plane.

Analytical representation

An equation or algebraic expression that defines the function (e.g., y = f(x)).

Numerical representation

A table listing input-output pairs (x, f(x)).

Verbal representation

A description of the function's rule or behavior in words.

Increasing

As the input increases, the output increases; if a < b then f(a) < f(b).

Decreasing

As the input increases, the output decreases; if a < b then f(a) > f(b).

Rate of change (slope)

The rate at which the output changes with respect to the input; the slope of the graph.

Concave up

The graph curves upward; the rate of change is increasing.

Concave down

The graph curves downward; the rate of change is decreasing.

Midline

The horizontal line through a periodic graph representing its central value around which the graph oscillates.

Piecewise function

A function defined by different rules on different intervals.

Interval

A set of real numbers between two endpoints, typically written (a,b), [a,b], etc.

Polar functions

Functions described in polar coordinates; their graphs may be functions even if they fail the vertical line test.