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Introduction to Inverse Functions quiz

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  • What is a one-to-one function?
    A one-to-one function is a function where each output (y value) is paired with at most one input (x value).
  • How can you quickly check if a function is one-to-one using ordered pairs?
    Check if any output value is repeated; if so, the function is not one-to-one.
  • What test do you use on a graph to determine if a function is one-to-one?
    You use the horizontal line test; if any horizontal line passes through more than one point, the function is not one-to-one.
  • What does the notation f⁻¹ represent?
    The notation f⁻¹ represents the inverse function of f, not 1 over f.
  • How do you form the inverse of a function given as ordered pairs?
    Swap each ordered pair's x and y values to create the inverse function.
  • What happens to the domain and range when forming the inverse of a function?
    The domain and range swap; the original domain becomes the inverse's range, and the original range becomes the inverse's domain.
  • Why can't all functions have inverses?
    Only one-to-one functions have inverses because otherwise, the inverse would not be a function.
  • What is the key feature of a correspondence diagram for a one-to-one function?
    Each output has at most one arrow coming in from an input.
  • How does the horizontal line test relate to the definition of a one-to-one function?
    If a horizontal line crosses the graph more than once, it means an output is paired with multiple inputs, so the function is not one-to-one.
  • What is the difference between the vertical and horizontal line tests?
    The vertical line test checks if a graph is a function, while the horizontal line test checks if it is one-to-one.
  • If a function f has ordered pairs (a, b), what are the ordered pairs for its inverse?
    The inverse will have ordered pairs (b, a).
  • What does it mean if two inputs in a function have the same output?
    It means the function is not one-to-one.
  • How can you use a list of outputs to check if a function is one-to-one?
    Look for repeated outputs; if any output is repeated, the function is not one-to-one.
  • Why is understanding one-to-one functions important for inverse functions?
    Because only one-to-one functions have inverses that are also functions.
  • What does swapping inputs and outputs in a function accomplish?
    It creates the inverse function, reversing the roles of domain and range.