Algebra I: Chapter 3 Flashcards

Key Concepts in Relations, Functions, and Graphing

• Dependent Variable: Its value is influenced by the independent variable in a relation.
• Function: A specific type of relation; each input is associated with exactly one output.
• Independent Variable: The variable that determines the output’s value in a functions’ relation.

Types of Equations and Functions

• Linear Equation: Contains variables without exponents other than 1; graphs to a straight line.
• Linear Function: A function whose graph results in a straight line, representing a constant rate of change.
• Nonlinear Function: A function whose graph does not form a straight line, indicating a variable rate of change.

Graphing Essentials

• Vertical Line Test: A method to verify if a relation is a function; any vertical line should intersect the graph at most once per x-value.
• Coordinate Plane: The grid where points are plotted, formed by intersecting horizontal (x-axis) and vertical (y-axis) number lines.
• Ordered Pair: A coordinate representation in the form (x, y), indicating a point's position on the plane.

Components of Functions

• Domain: The complete set of x-coordinates (input values) from all ordered pairs in a function.
• Range: The complete set of y-coordinates (output values) derived from the range of the independent variable.
• Origin: The central point (0,0) on the coordinate plane where the x-axis and y-axis intersect.

Types of Functions

• Discrete Function: Represented by separate points; the graph does not connect them.
• Continuous Function: Illustrated by a smooth line or curve; indicates a complete range of values.
• Exponential Function: Function expressed as y = a^x, where a is a positive constant not equal to one.
• Quadratic Function: Defined by the form y = ax² + bx + c, with the coefficient 'a' being non-zero.

Additional Concepts

• Function Notation: A way to denote functions using symbols, such as f(x) = 3x - 8.
• Mapping: A visual representation showing how each value in the domain relates to a value in the range.
• Parabola: The graphical representation of quadratic functions typically U-shaped.