Module 4 Study Guide: Functions, Linear Forms, and Modeling

Vocabulary flashcards covering linear functions, intercepts, point-slope and slope-intercept forms, vertical and horizontal line relations, and real-world linear modeling.

Function

A relation that has exactly one element in the range for every value in its domain (for every $x$, there is only $1$ $y$, meaning no repeating $x$).

Zero of a Function

Another name for the $x$-intercept of a function, representing the point $(x, 0)$.

Point-Slope Form

The linear equation form represented by $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a given point on the line.

Slope-Intercept Form

The linear equation form represented by $y = mx + b$, where $m$ is the slope ($\frac{\text{Rise}}{\text{Run}}$) and $b$ is the $y$-intercept.

HOY

A mnemonic representing a horizontal line relation that is a function because every input in the domain has exactly one output in the range.

VUX

A mnemonic representing a vertical line relation that is not a function because a single value in the domain (such as $x = 1$) has an infinite number of outputs in the range.

Enrico's Savings Account Model

The linear function $y = 25x + 20$, which models account savings over time after starting with an initial opening balance of \twenty dollars ($\$20$) and depositing an additional \twenty-five dollars ($\$25$) per week.