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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 (x-value) has at most one output (y-value), while a relation can have inputs with multiple outputs.
  • How can you determine if a graph represents a function using the vertical line test?
    If any vertical line passes through more than one point on the graph, it is not a function; if every vertical line passes through at most one point, it is a function.
  • What is the first step when verifying if an equation is a function?
    The first step is to solve the equation for y in terms of x.
  • What does it mean if, after solving for y, a single x-value gives multiple y-values?
    It means the equation does not represent a function.
  • Why is the equation y = 3x - 4 a function?
    Because for every x-value, there is exactly one corresponding y-value.
  • Why is the equation x^2 + y^2 = 25 not a function?
    Because for some x-values, there are two possible y-values (one positive and one negative), so it fails the function test.
  • What is function notation and when can you use it?
    Function notation replaces y with f(x) and can only be used if the equation represents a function.
  • What does the 'squish strategy' help you find on a graph?
    Squishing the graph to the x-axis finds the domain, and squishing to the y-axis finds the range.
  • How do you express the domain and range using interval notation?
    Interval notation uses brackets [ ] for included values and parentheses ( ) for excluded values to show the range of x or y values.
  • What does a closed dot or solid line on a graph indicate about domain or range?
    It indicates that the value is included in the domain or range.
  • What does an open circle on a graph indicate about domain or range?
    It means that the value is not included in the domain or range.
  • What are two common restrictions when finding the domain of an equation?
    You cannot have negative values under a square root or zero in the denominator of a fraction.
  • What is the domain of f(x) = √x in interval notation?
    The domain is [0, ∞), meaning x must be greater than or equal to 0.
  • What is the domain of f(x) = 2/(x - 5) in interval notation?
    The domain is (-∞, 5) ∪ (5, ∞), meaning all real numbers except x = 5.
  • When do you use a union symbol (∪) in interval notation for domain or range?
    You use a union symbol when the domain or range consists of multiple, separate intervals.