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Precalculus: Relations and Functions

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Termini in questo insieme (20)

  • What is a relation in mathematics?
    A relation is any set of ordered pairs.
  • Define the domain of a relation.
    The domain is the set of all first components (x-values) of the ordered pairs.
  • Define the range of a relation.
    The range is the set of all second components (y-values) of the ordered pairs.
  • What makes a relation a function?
    A relation is a function if each element in the domain corresponds to exactly one element in the range.
  • How can you identify a function from a set of ordered pairs?
    If no x-value repeats with different y-values, the set is a function.
  • What is the Vertical Line Test?
    If any vertical line intersects a graph more than once, the graph does not represent a function.
  • How do you evaluate a function at a given value?
    Substitute the given value for x in the function's expression and simplify.
  • What is the difference between independent and dependent variables in a function?
    The independent variable (x) can be any value; the dependent variable (y or f(x)) depends on x.
  • How is function notation written?
    Function notation is written as \(f(x)\), representing the output for input x.
  • What does the domain represent on a graph?
    The domain is the set of all x-values (inputs) shown on the graph.
  • What does the range represent on a graph?
    The range is the set of all y-values (outputs) shown on the graph.
  • How is interval notation used for domain and range?
    Square brackets [ ] include endpoints; parentheses ( ) exclude endpoints; parentheses are used with infinity.
  • What does it mean if an equation solved for y gives more than one y for a given x?
    The equation is not a function.
  • Is the equation \(x + y = 4\) a function?
    Yes, y can be expressed as y = 4 - x, which gives one y for each x.
  • Is the equation \(y^2 = 5x\) a function?
    No, solving for y gives two values (positive and negative) for some x-values.
  • What are x-intercepts of a function?
    Points where the graph crosses the x-axis; function values at these points are zero.
  • Can a function have more than one y-intercept?
    No, a function can have only one y-intercept.
  • How do you determine if a graph represents a function using the Vertical Line Test?
    If any vertical line crosses the graph more than once, it is not a function.
  • What is the domain of the function graphed from x = -2 to x = 3 including -2 but excluding 3?
    The domain is \([-2, 3)\).
  • What is the range of the function graphed from y = 1 to y = 4 including 1 but excluding 4?
    The range is \([1, 4)\).