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Introduction to Relations and Functions quiz

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  • What is a relation in mathematics?
    A relation is a connection between inputs (x-values) and outputs (y-values), often represented as ordered pairs.
  • How can relations be represented?
    Relations can be represented as ordered pairs, tables, graphs, equations, or correspondences.
  • What makes a relation a function?
    A function is a relation where each input (x-value) is paired with exactly one output (y-value).
  • How do you determine if a relation is not a function using ordered pairs?
    If any input (x-value) is paired with more than one output (y-value), the relation is not a function.
  • What is the vertical line test?
    The vertical line test is a method to determine if a graph represents a function by checking if any vertical line crosses the graph more than once.
  • What does it mean if a vertical line crosses a graph more than once?
    If a vertical line crosses a graph more than once, the graph does not represent a function.
  • What is the domain of a relation or function?
    The domain is the set of all input values (x-values) for a relation or function.
  • What is the range of a relation or function?
    The range is the set of all output values (y-values) for a relation or function.
  • How do you find the domain and range from a table of values?
    List all the x-values for the domain and all the y-values for the range, without repeating any values.
  • How do you express the domain and range for a continuous graph?
    For continuous graphs, domain and range are expressed using interval notation to capture all possible x and y values within specified bounds.
  • What symbol is used in interval notation to include an endpoint?
    A bracket [ or ] is used to include an endpoint in interval notation.
  • What symbol is used in interval notation to exclude infinity?
    A parenthesis ( or ) is used to exclude infinity in interval notation.
  • If a graph starts at x = -4 and continues to infinity, how is the domain written in interval notation?
    The domain is written as [−4, ∞) in interval notation.
  • If a graph starts at y = -2 and continues to infinity, how is the range written in interval notation?
    The range is written as [−2, ∞) in interval notation.
  • Are all functions relations, and are all relations functions?
    All functions are relations, but not all relations are functions.