Graphs of Functions - Vocabulary

Vocabulary flashcards covering graphs of functions, their types, key concepts, and the vertical line test from the Graphs of Functions section.

Graph of a function

The set of all ordered pairs (x, y) in the coordinate plane with y = f(x).

Domain

The set of input values x for which f(x) is defined.

Input

An x-value used as the argument to a function.

Output

The y-value produced by the function for a given input x (i.e., f(x)).

Linear function

A function of the form f(x) = mx + b; its graph is a straight line with slope m and y-intercept b.

Slope

The rate of change of a linear function; the coefficient m in f(x) = mx + b (rise over run).

y-intercept

The y-value when x = 0; the constant term b in f(x) = mx + b; where the graph crosses the y-axis.

Constant function

A function f(x) = b; its graph is a horizontal line y = b.

Power function

A function of the form f(x) = x^n; examples include x^2, x^3, etc.

Root function

A function of the form f(x) = x^(1/n) (nth root); graphs are root curves.

Reciprocal function

A function f(x) = 1/x; its graph is a hyperbola with vertical and horizontal asymptotes.

Absolute value function

f(x) = |x|; graph is V-shaped with vertex at the origin.

Floor function

f(x) = ⌊x⌋; greatest integer less than or equal to x.

Ceiling function

f(x) = ⌈x⌉; smallest integer greater than or equal to x.

Piecewise defined function

A function defined by different formulas on different parts of its domain; graph consists of separate pieces.

Vertical Line Test

A curve is the graph of a function iff no vertical line intersects the curve more than once.

Graphing calculator

A calculator used to graph functions (e.g., TI-83); helps plot y = f(x).

Equation form

An equation in x and y that expresses a relationship; not every such equation defines y as a function of x.

Function form

An equation written as y = f(x), expressing y as a function of x.

Solving for y

Isolating y in an equation to determine whether it defines y as a function of x (one y for each x).

Graphing by plotting points

A method to graph f by plotting points (x, f(x)) and connecting them with a smooth curve.