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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 distinguishes a function from a general relation?
    A function is a relation where each input corresponds to exactly one output.
  • What is the vertical line test used for?
    The vertical line test is used 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, or 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, or y-values, for a relation or function.
  • How do you find the domain from a set of ordered pairs?
    List all the x-values from the ordered pairs, making sure not to repeat any values.
  • How do you find the range from a set of ordered pairs?
    List all the y-values from the ordered pairs, without repeating any values.
  • What is interval notation used for in domain and range?
    Interval notation is used to express the domain and range for continuous graphs, indicating the span of x and y values covered.
  • How do you write the domain and range for a continuous graph?
    Use interval notation to show the starting and ending values for x (domain) and y (range), including or excluding endpoints as appropriate.
  • What does a solid dot on a graph indicate when using interval notation?
    A solid dot means the endpoint is included in the interval, so use a bracket in interval notation.
  • What does infinity mean in interval notation for domain or range?
    Infinity indicates the domain or range extends without bound, and is always excluded using a parenthesis.
  • Can a relation be a function if an input is paired with more than one output?
    No, a function requires each input to be paired with only one output.
  • Are all functions relations?
    Yes, all functions are relations, but not all relations are functions.