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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 for different input values; if so, the function is not one-to-one.
  • What test is used on a graph to determine if a function is one-to-one?
    The horizontal line test is used; if any horizontal line passes through more than one point, the function is not one-to-one.
  • What does the notation f⁻¹ represent?
    f⁻¹ represents the inverse function of f, not the reciprocal or 1/f.
  • How do you form the ordered pairs of an inverse function from the original function?
    You swap the x and y values in each ordered pair of the original function to get the inverse.
  • What happens to the domain and range when forming the inverse of a function?
    The domain and range swap; the domain of the original becomes the range of the inverse, and vice versa.
  • Why can't a function with two inputs mapping to the same output be one-to-one?
    Because a one-to-one function requires each output to be paired with at most one input.
  • What is the significance of the horizontal line test passing for a function?
    It means the function is one-to-one and thus has an inverse function.
  • If a function fails the vertical line test, what does that mean?
    It means the relation is not a function.
  • What is the main difference between the vertical and horizontal line tests?
    The vertical line test checks if a relation is a function, while the horizontal line test checks if a function is one-to-one.
  • How is the inverse function related to the original function in terms of mapping?
    The inverse function reverses the mapping, swapping inputs and outputs.
  • What does it mean if a function's graph has a horizontal line passing through two points?
    It means the function is not one-to-one.
  • Why is it important to distinguish between f⁻¹ and 1/f?
    Because f⁻¹ denotes the inverse function, not the reciprocal of f.
  • What is a quick way to spot a non-one-to-one function in a correspondence diagram?
    Look for two arrows from different inputs pointing to the same output.
  • Why do only one-to-one functions have inverses?
    Because only one-to-one functions allow each output to be uniquely mapped back to an input.