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Properties of Functions definitions

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  • Maximum Value
    The highest output a function attains, occurring at a specific input where all other outputs are less than or equal to this value.
  • Minimum Value
    The lowest output a function reaches, found at an input where all other outputs are greater than or equal to this value.
  • Increasing Function
    A graph where outputs rise as inputs move from left to right, resembling an upward walk along the curve.
  • Decreasing Function
    A graph where outputs fall as inputs move from left to right, similar to a downward walk along the curve.
  • Constant Function
    A graph that remains flat, producing the same output for every input, with no upward or downward trend.
  • Y-Axis Symmetry
    A property where folding the graph along the y-axis aligns both sides perfectly, indicating identical outputs for opposite inputs.
  • Even Function
    A function where substituting a negative input yields the same output as the positive input, reflecting y-axis symmetry.
  • Origin Symmetry
    A property where folding the graph over both axes aligns it, showing that outputs are mirrored and sign-reversed for opposite inputs.
  • Odd Function
    A function where the output for a negative input is the negative of the output for the positive input, reflecting origin symmetry.
  • X-Axis Symmetry
    A property where folding the graph along the x-axis aligns both sides, but this pattern never represents a function.
  • Vertical Line Test
    A method to determine if a graph represents a function by checking if any vertical line crosses the graph more than once.
  • Output
    The value produced by a function for a given input, often represented as the y-value on a graph.
  • Input
    The value substituted into a function, typically represented as the x-value on a graph.
  • Graph
    A visual representation of a function, illustrating the relationship between inputs and outputs.
  • Symmetry
    A characteristic where a graph remains unchanged after specific folds or reflections, revealing patterns in function behavior.