Functions, Transformations, and Graphs Vocabulary

Vocabulary flashcards covering domain, range, function transformations, and function properties based on the lecture material.

Domain

The set of all input values along the $x$-axis for which a function is defined.

Range

The set of all output values along the $y$-axis that a function reaches from its lowest bound to its highest bound.

Interval Notation

A notation system for representing domain and range where square brackets indicate included endpoints and parentheses indicate excluded endpoints.

Radical Function

A function containing an expression under a radical sign, where everything under the radical must be greater than or equal to $0$ for the function to be defined.

Coefficient

The number that multiplies a variable, located directly in front of the variable.

Linear Function

A function where the power of the variable $x$ is $1$, producing a straight line graph.

Piecewise-Defined Function

A function defined by different expressions or rules over different sub-intervals of its domain.

Function Composition

An operation denoted as $(f \circ g)(x) = f(g(x))$, where the output of $g(x)$ is used as the input into function $f$.

Reflection Across the x-axis

A transformation represented by $-f(x)$, which flips the graph of $f(x)$ vertically across the $x$-axis.

Reflection Across the y-axis

A transformation represented by $f(-x)$, which flips the graph of $f(x)$ horizontally across the $y$-axis.

Parent Function

The simplest form or base graph of a function family, such as $y = \sqrt{x}$ or $y = |x|$, before transformations are applied.

Absolute Value Function

A function defined using absolute value signs whose base parent graph forms a V-shape.

Even Function

A function that satisfies the algebraic condition $f(-x) = f(x)$ for every $x$ in its domain.

Odd Function

A function that satisfies the algebraic condition $f(-x) = -f(x)$ for every $x$ in its domain.

Horizontal Line Test

A visual test applied to a function graph to determine whether it is a one-to-one function.