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Intro to Functions & Their Graphs definitions Flashcards

Intro to Functions & Their Graphs definitions
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  • Relation
    A connection between x and y values, represented as ordered pairs, where each input may correspond to one or more outputs.
  • Function
    A special type of relation where each input is paired with at most one output, ensuring no input has multiple outputs.
  • Input
    The x-value in a relation or function, representing the independent variable or domain element.
  • Output
    The y-value in a relation or function, representing the dependent variable or range element.
  • Vertical Line Test
    A graphical method to determine if a graph represents a function by checking if any vertical line crosses more than one point.
  • Domain
    The set of all possible x-values for which a function or relation is defined, often found by identifying restrictions.
  • Range
    The set of all possible y-values that a function or relation can produce, determined from the graph or equation.
  • Interval Notation
    A way to express domains and ranges using brackets and parentheses to indicate included or excluded endpoints.
  • Set Builder Notation
    A notation using inequality symbols to describe the set of values that satisfy certain conditions for domain or range.
  • Function Notation
    A symbolic way to represent functions, typically using f(x) instead of y, to clarify input-output relationships.
  • Slope-Intercept Form
    An equation format y = mx + b, where m is the slope and b is the y-intercept, always representing a function.
  • Restriction
    A value or condition that is excluded from the domain, often due to division by zero or negative values under a square root.
  • Union Symbol
    A symbol (∪) used in interval notation to combine multiple intervals when the domain or range has gaps.
  • Open Circle
    A graphical indicator showing that a specific endpoint is not included in the domain or range.
  • Closed Circle
    A graphical indicator showing that a specific endpoint is included in the domain or range.