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Graphing Exponential Functions quiz

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  • What is the y-intercept of the exponential function f(x) = 2^x?
    The y-intercept is at (0, 1) because 2^0 = 1.
  • As x approaches negative infinity in f(x) = 2^x, what value does f(x) approach?
    f(x) approaches 0, creating a horizontal asymptote at y = 0.
  • What is the domain of any exponential function of the form f(x) = b^x?
    The domain is all real numbers, or (-∞, ∞).
  • How does the value of the base b affect the direction of the graph of f(x) = b^x?
    If b > 1, the graph increases; if 0 < b < 1, the graph decreases.
  • What is the range of f(x) = 2^x?
    The range is (0, ∞) because the graph never touches or goes below y = 0.
  • What does a negative sign outside the exponential function indicate?
    It indicates a reflection over the x-axis.
  • What does a negative sign inside the exponent of an exponential function indicate?
    It indicates a reflection over the y-axis.
  • How do you graph a transformed exponential function like g(x) = 2^(x-1) - 4?
    Start with the parent function, shift the graph right by 1 and down by 4, and adjust the horizontal asymptote to y = -4.
  • What is the horizontal asymptote of f(x) = 2^x?
    The horizontal asymptote is y = 0.
  • How do you determine the range of a transformed exponential function?
    The range depends on the position of the graph relative to the new asymptote; if above, it's (k, ∞), if below, it's (-∞, k).
  • What is the effect of increasing the base b in f(x) = b^x when b > 1?
    The graph becomes steeper as b increases.
  • What is the effect of decreasing the base b in f(x) = b^x when 0 < b < 1?
    The graph becomes steeper as b decreases toward zero.
  • What is the first step when graphing a transformed exponential function?
    Graph the parent function first before applying any transformations.
  • How do you shift the horizontal asymptote when graphing g(x) = b^(x-h) + k?
    Shift the horizontal asymptote from y = 0 to y = k.
  • What does it mean for an exponential function to be one-to-one?
    It means that no two x-values produce the same y-value, so the graph passes the horizontal line test.