Algebra 2 - Test #1 Review: Equations, Functions, Lines, and Transformations

Vocabulary practice flashcards covering core algebraic concepts, linear forms, absolute value properties, function notation, transformations, and systems from the Algebra 2 Test #1 Review Packet.

Point-Slope Form

A linear equation format written as $y - y_1 = m(x - x_1)$, where $m$ represents the slope and $(x_1, y_1)$ represents a known point on the line.

Slope-Intercept Form

A linear equation format expressed as $y = mx + b$, where $m$ denotes the slope and $b$ denotes the y-intercept of the line.

Vertex of an Absolute Value Function

The maximum or minimum point $(h, k)$ of the absolute value function $y = a|x - h| + k$, representing the point where the graph changes direction.

Line of Symmetry

The vertical line given by $x = h$ that passes directly through the vertex of an absolute value graph and divides the graph into two symmetrical, mirror-image halves.

Piecewise Function

A function composed of multiple sub-functions, each applied to a distinct interval or domain piece of the independent variable.

Domain

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

Range

The complete set of all possible output values or $y$-values produced by a function or relation across its domain.

Function

A specific type of relation in which each input value in the domain is paired with exactly one output value in the range.

Evaluating a Function

The process of substituting a specific input value in place of the variable $x$ within a function's rule to compute the resulting output value.

Compound Inequality

An inequality formed by combining two separate inequality statements using the conjunction 'and' (intersection of sets) or 'or' (union of sets).

Interval Notation

A method of writing solution sets for inequalities using brackets ($[\,]$) to indicate included boundary values and parentheses (($()$) to indicate excluded boundary values or infinity.

System of Equations

A set of two or more equations containing the same variables that are solved simultaneously to identify common solutions or points of intersection.

System of Inequalities

A set of two or more inequalities sharing the same variables whose solution is represented graphically by the region where the shaded solution areas overlap.

Horizontal Translation

A transformation that shifts a graph left or right, represented in function notation by $f(x - h)$ (shifting right by $h$ units) or $f(x + h)$ (shifting left by $h$ units).

Vertical Translation

A transformation that shifts a graph upward or downward without changing its shape, represented by adding or subtracting a constant outside the function, such as $f(x) + k$ or $f(x) - k$.

Vertical Compression

A transformation that scales the graph vertically toward the x-axis by a factor $a$, occurring when the coefficient satisfies $0 < |a| < 1$.

Vertical Reflection

A transformation resulting from multiplying a function by $-1$, flipping the graph upside down across a horizontal axis of reflection.

Perpendicular Lines

Lines that intersect at right angles ($90^\circ$), having slopes that are negative reciprocals of each other such that $m_1 \times m_2 = -1$.