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Intro to Functions & Their Graphs quiz

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  • What is the main difference between a relation and a function?
    A function is a special type of relation where each input has at most one output; not all relations are functions.
  • How can you visually determine if a graph represents a function?
    You can use the vertical line test: if any vertical line passes through more than one point on the graph, it is not a function.
  • What does it mean if an input in a relation has more than one output?
    It means the relation is not a function because functions require each input to have at most one output.
  • What is the first step when verifying if an equation is a function?
    The first step is to solve the equation for y.
  • What do you check for after solving an equation for y to determine if it is a function?
    You check if any x-value results in multiple y-values; if so, it is not a function.
  • Are all linear equations of the form y = mx + b functions?
    Yes, all linear equations with a defined slope are functions because each x-value gives exactly one y-value.
  • What does the notation f(x) represent in function notation?
    f(x) replaces y and represents the output of the function for a given input x.
  • How do you find the domain of a function from its graph?
    Squish the graph down to the x-axis; the resulting interval shows the domain.
  • How do you find the range of a function from its graph?
    Squish the graph down to the y-axis; the resulting interval shows the range.
  • What does a closed dot or solid line on a graph indicate about domain or range?
    A closed dot or solid line means the endpoint is included in the domain or range.
  • What does an open circle on a graph indicate about domain or range?
    An open circle means the endpoint is not included in the domain or range.
  • What are the two common notations for expressing domain and range?
    Domain and range can be expressed using interval notation or set builder notation.
  • What restriction is placed on the domain when x is inside a square root?
    The domain is restricted to values where the inside of the square root is not negative.
  • What restriction is placed on the domain when x is in the denominator of a fraction?
    The domain excludes any x-values that make the denominator zero.
  • How do you express the domain of f(x) = 2/(x-5) in interval notation?
    The domain is (-∞, 5) ∪ (5, ∞), meaning all real numbers except x = 5.