Graphing Concepts in Algebra 1

Graphing Concepts in Algebra 1

• Continuous Graph: Characterized by no breaks or interruptions; represents a smooth connection between points.
• Relation: A systematic pairing of input values (domain) with output values (range).
• Domain: The complete set of all possible input values in a given relation.
• Range: The complete set of all possible output values corresponding to the inputs in a relation.
• Discrete Graph: Composed of distinct, isolated points rather than connected lines.
• Vertical Line Test: A method for determining if a graph is a function; if any vertical line intersects the graph more than once, it is not a function.
• Function: A specific relation where each input has a unique output; crucial for defining mathematical operations.
• Function Notation: A standardized way of expressing functions algebraically, frequently using symbols like f(x).

Types of Functions

• Increasing Function: A function where the output values rise as the input values increase across the entire domain.
• Decreasing Function: A function where the output values decline as the input values increase across the entire domain.
• Constant Function: A function whose output remains unchanged regardless of input variability.
• Function Family: A collection of functions that share common features or behaviors.
• Linear Functions: Functions that produce straight-line graphs, typically represented in the form f(x) = mx + b, where m and b are real numbers.
• Exponential Functions: Functions in the form f(x) = a * b^(x), where a and b are real numbers, b is greater than zero, and b is not equal to one.

Function Characteristics

• Absolute Minimum: The lowest point on a graph, characterized by the smallest y-coordinate compared to all other points.
• Dependent Quantity: A variable whose value is determined by another variable; reflects the outcome of a function.
• Independent Quantity: The variable that influences or determines the value of the dependent quantity.
• Absolute Maximum: The highest point on a graph, characterized by the largest y-coordinate among all points.
• Linear Absolute Value: Represents the distance of a number from zero on the number line, reflecting its non-negative value.
• Linear Piecewise Function: Functions defined by multiple equations, each applicable to different segments of the domain.
• Quadratic Functions: Functions that follow the standard form f(x) = ax² + bx + c, where a, b, and c are real numbers and a is non-zero, typically producing parabolic graphs.