Algebra 2: Functions, Domain, Range, and Average Rate of Change

This set of vocabulary flashcards covers the foundational concepts of functions, including notation, graphical tests, domain and range restrictions, mathematical notations, and the calculation of average rate of change.

Function

A relation that assigns each input to exactly one output.

Vertical Line Test

A method to check if a graph represents a function by dragging an imaginary vertical line across it; if the line crosses the graph more than once, it is not a function.

Input Variable

The independent variable, represented by the value inside the parentheses in function notation, such as $x$ in $f(x)$, $t$ in $w(t)$, or $r$ in $g(r)$.

Output Variable

The dependent variable, represented by the value outside the parentheses in function notation, signifying the result that depends on the input.

Domain

The set of all possible input values ($x$ values) for a function; what you are allowed to put into the equation.

Range

The set of all possible output values ($y$ values) of a function; the values that come out when inputs are put into the equation.

Radicand Restriction

A restriction where the value inside a square root (or any even-index radical) cannot be negative, requiring $\text{radicand} \neq \text{negative}$ or $\text{radicand} \triangle 0$.

Denominator Restriction

A restriction stating that a fraction cannot have a zero in the denominator; the denominator must satisfy the condition $\text{denominator} \neq 0$.

Set-Builder Notation

A standard mathematical notation used to describe a set by stating a rule or condition, written as $\{ \text{variable} | \text{condition} \}$, which is read as 'the set of all values such that…'

Interval Notation

A way to describe sets of numbers using brackets $[ \text{ } ]$ for closed values (equal to) and parentheses $( \text{ } )$ for open values (not equal to) or infinity.

Average Rate of Change

The ratio of the change in output to the change in input between two points, calculated as $\frac{\text{Output}_2 - \text{Output}_1}{\text{Input}_2 - \text{Input}_1}$ or $\frac{y_2 - y_1}{x_2 - x_1}$.

Secant Line

A line connecting two points on a graph whose slope is equivalent to the average rate of change between those two points.

$$x \triangle \text{R}$$

A symbol used in set-builder notation meaning '$x$ is a real number'.