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Properties of Functions quiz

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  • What is the maximum value of a function?
    The maximum value is the highest output (y value) that the function attains for some input x.
  • What does the minimum value of a function represent?
    The minimum value is the lowest output (y value) that the function attains for some input x.
  • How can you identify an increasing function by looking at its graph?
    An increasing function has a graph that rises as you move from left to right.
  • What is a decreasing function?
    A decreasing function is one whose graph falls as you move from left to right.
  • What does it mean for a function to be constant?
    A constant function has the same output for every input, resulting in a flat, horizontal graph.
  • What type of symmetry does an even function have?
    An even function has symmetry about the y-axis.
  • How do you test if a function is even using its formula?
    A function is even if f(-x) = f(x) for all x in its domain.
  • What is the defining property of an odd function?
    An odd function satisfies f(-x) = -f(x) for all x in its domain.
  • What kind of symmetry does an odd function display?
    An odd function is symmetric about the origin.
  • What does symmetry about the x-axis indicate about a graph?
    Symmetry about the x-axis means the graph is not a function, since one x value gives multiple y outputs.
  • What is the vertical line test used for?
    The vertical line test determines if a graph represents a function; if any vertical line crosses the graph more than once, it is not a function.
  • If a graph is flat and horizontal, what type of function does it represent?
    It represents a constant function, where the output does not change as the input changes.
  • What happens to the output of an even function when you input x and -x?
    The output is the same for both x and -x in an even function.
  • How do the outputs of an odd function at x and -x relate?
    The output at -x is the negative of the output at x for an odd function.
  • Why is a graph with x-axis symmetry not a function?
    Because it assigns more than one output to a single input, violating the definition of a function.