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.

This quiz covers essential graphing concepts in Algebra 1, including definitions and characteristics of continuous and discrete graphs. You will also explore key terms such as functions, domain, range, and the vertical line test. Test your understanding of these foundational concepts in algebra.