Functions and Their Properties

A collection of vocabulary flashcards covering key concepts in the functions and their properties, algebraic manipulation, and solving inequalities.

Domain

The set of all possible input values (x-values) for which a function is defined.

Linear Functions

Functions where the domain is all real numbers (-∞, ∞).

Radical Functions

Functions where the expression inside the radical must be greater than 0.

Logarithmic Functions

Functions where the argument of the logarithm must be greater than 0.

Rational Functions

Functions where the denominator cannot be equal to 0.

Circle Equations

Equations where the domain is restricted by the radius and center.

Symmetry

Characteristics describing whether a function is even (symmetric about y-axis) or odd (symmetric about origin).

Inverse Functions

Functions where f(g(x)) = x and g(f(x)) = x.

Transformations of Functions

Modifying a parent function to create a new graph, through stretches, compressions, shifts, etc.

Stretches and Compressions

Vertical (a f(x)) and horizontal (f(b·x)) modifications of a parent function.

One-to-One Functions

Functions where each output corresponds to exactly one input, passing the Horizontal Line Test.

Algebraic Manipulation

The process of simplifying and rewriting algebraic expressions.

Simplifying Rational Expressions

Involves factoring and canceling common terms.

Completing the Square

Rewriting quadratics in the form a(x − h)² + k.

Solving Inequalities

Finding the range of values that satisfy an inequality.

Linear Inequalities

Inequalities where you must isolate the variable, flipping the sign when multiplying/dividing by a negative.

Polynomial Inequalities

Involves finding zeros, creating a sign chart, and testing intervals.

Number-Line Graphs

Graphs that use open circles for strict inequalities and closed circles for inclusive inequalities.