Limits and Graphs (L1 Standard) - Vocabulary Flashcards

Vocabulary flashcards covering key terms from Limits and Graphs notes.

Function

A relation that assigns to each element x in its domain exactly one output f(x); commonly represented by a graph, table, or equation.

Domain

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

Range

The set of all possible outputs f(x) as x varies over the domain.

Graph

The graphical representation of a function, i.e., the set of ordered pairs (x, f(x)).

Increasing on an interval

A function is increasing on an interval I if for any x1 < x2 in I, f(x1) < f(x2).

Decreasing on an interval

A function is decreasing on an interval I if for any x1 < x2 in I, f(x1) > f(x2).

Vertical Line Test

A graph represents a function only if every vertical line intersects it at most once.

x-intercept

The x-coordinate(s) where the graph crosses the x-axis; values satisfying f(x) = 0.

y-intercept

The y-coordinate where the graph crosses the y-axis; equal to f(0).

Limit

The value L that f(x) can be made arbitrarily close to by taking x sufficiently close to a (x → a).

Left-hand limit

The limit of f(x) as x approaches a from the left side: lim x→a− f(x) = L.

Right-hand limit

The limit of f(x) as x approaches a from the right side: lim x→a+ f(x) = L.

Limit exists

The limit lim x→a f(x) exists when the left-hand and right-hand limits both exist and are equal to the same real number L.

Infinite limit

A limit where f(x) grows without bound as x approaches a (lim x→a f(x) = ∞ or -∞).

Vertical asymptote

A vertical line x = a where f(x) → ±∞ as x → a.

Horizontal asymptote

A horizontal line y = L that f(x) approaches as x → ±∞.

End behavior

The behavior of f(x) as x → ±∞ or as x approaches a limit at infinity.

Removable discontinuity

A hole in the graph at x = a where the limit exists but f(a) ≠ L (or is undefined); can be fixed by redefining f(a) = L.

Piecewise-defined function

A function defined by different formulas on different parts of its domain.

f(x) notation

The output value of the function corresponding to input x; f(x) is the function's rule applied to x.

Function rule

The explicit formula that defines f(x), e.g., f(x) = x^2 + 3x − 4.

Graph as set of ordered pairs

The graph is the set { (x, f(x)) | x ∈ D }.