Algebra I Review: Linear Functions, Transformations, and Equations

Vocabulary practice flashcards covering fundamental Algebra I concepts including function transformations, linear equations, intercepts, slopes, domain, range, and inequalities.

Horizontal Translation

A rigid shift of a function's graph to the left or right, created by adding or subtracting a constant inside the grouping symbol of the function (for example, $g(x) = |x - 1|$ shifts the parent graph 1 unit to the right).

Vertical Translation

A rigid shift of a function's graph up or down, created by adding or subtracting a constant outside the grouping symbol of the function (for example, $g(x) = |x| + 3$ shifts the parent graph 3 units up).

Slope-Intercept Form

A linear equation written in the form $y = mx + b$, where $m$ represents the slope (rate of change) and $b$ represents the $y$-intercept.

Standard Form of a Linear Equation

A linear equation expressed as $Ax + By = C$, where $A$, $B$, and $C$ are integers with no common factors, and $A$ is typically non-negative.

$x$-Intercept

The point where the graph of a line or curve intersects the $x$-axis, found algebraically by substituting $y = 0$ into the equation.

$y$-Intercept

The point where the graph of a line or curve intersects the $y$-axis, found algebraically by substituting $x = 0$ into the equation.

Perpendicular Lines

Lines that intersect at a right angle ($90^\circ$) and have slopes that are opposite reciprocals, such that their product equals $-1$, or where one line is horizontal (slope of $0$) and the other is vertical (undefined slope).

Parallel Lines

Lines that lie in the same plane and never intersect, characterized by having identical slopes.

Domain

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

Range

The set of all possible output values ($y$-values) that result from the input values of a relation or function.

Average Rate of Change

The ratio that describes how much the dependent variable changes relative to the independent variable over a specific interval, calculated as $\frac{\Delta y}{\Delta x} = \frac{f(b) - f(a)}{b - a}$.

Vertex of an Absolute Value Function

The maximum or minimum turning point $(h, k)$ of the V-shaped graph of an absolute value function.

Axis of Symmetry

A vertical line given by $x = h$ that passes through the vertex of a symmetric graph, dividing it into two mirror-image halves.

Compound Inequality

An inequality formed by combining two separate inequalities with the word 'and' or 'or' (for example, $-9 < 3 + \frac{x}{3} < 3$).

Literal Equation

An equation consisting primarily of multiple variables or letters (such as formulas like $V = \pi r^2 h$ or $F = ma$) that can be rearranged to solve for a specific variable.