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Rational Functions

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  • What is the domain of this function?
    All real numbers
    x = 1, -1
    All reals except x = -4, 1
    All reals except x = 1, -1
  • Where is/are the x-intercept(s) of this function?
    x = 4
    y = 8
    x = -1
    x = -1, 4
  • Where are the holes in the following function?
    Swiss Cheese
    At the origin
    There are none
    x = 4, -4
  • Setting the denominator equal to zero and solving will help you find...
    Horizontal Asymptotes
    Vertical Asymptotes
    Holes and Vertical Asymptotes
    Holes
  • Holes occur when the value of a rational function is...
    0/0
    0
    1/0
    x/0
  • Vertical Asymptotes are always written in the form...
    x = #
    y = mx + b
    y = #
    Chuck Norris
  • What are the x-intercepts of the following function?
    x = 0, 4, -4
    There are none
    x = 0, 16
    x = 4, -4
  • If the denominator's degree is bigger than the numerator's degree, Horizontal Asymptote is...
    There is none
    x = 0
    y = 1
    y = 0
  • When the numerator's degree is bigger, the Horizontal Asymptote is...
    There is none
    y = 0
    x = 0
    Infinity
  • Evaluating a rational function at zero is the best way to determine where...
    the holes are
    to go for fresh produce
    the y-intercept is
    the x-intercepts are
  • Excluded values resulting from factors that can NOT be canceled will cause...
    Vertical Asymptotes
    Horizontal Asymptotes
    Tsunamis in 3rd World countries
    Holes
  • Where are the x-intercepts in the following graph...
    x = -2/3
    x = 4
    x = -2
    x = 2
  • Describe the domain of the following function...
    All reals except x = -1, 5
    All reals except x = -3, 2
    All reals except x = -2, 3
    All reals except x = -5, 1
  • Setting the numerator equal to zero and solving will help you find...
    Excluded Values
    Purpose in life
    Y-intercepts
    X-Intercepts
  • What are x = -3 and x = 4
    My favorite numbers
    The vertical asymptotes
    The x-intercepts
    The holes
  • Find the Horizontal Asymptote
    x = 0 
    y = -2
    y = 0
    x = -2
  • The horizontal asymptote will be equal to the ratio of its leading coefficients when
    the degree on the bottom is bigger
    when the degrees are the same
    the degree on the top is bigger
    98 Degrees was a great band
  • Where is the y-intercept of this function?
    x = -8
    y = -8
    x = 8
    y = 8
  • Horizontal Asymptotes are always written in the form....
    Horizontal whaa?
    y = #
    x = #
    Take the L.
  • Find the Horizontal Asymptote of this function...
    There is none
    y = -1/4
    x = -1/4
    y = 1/4
  • Where is the vertical asymptote of this function?
    x = 4, -1
    x = -1
    x = 1, -1
    x = 1
  • Where is the y-intercept in the following function?
    y = 1/4
    Witness protection
    0
    There's a hole there
  • Find the holes (if any) in the following function...
    x = 4
    x = 2, -1
    There are none
    x = -2, 1
  • What is the Horizontal Asymptote of the function
    There is none
    y = -1/3
    y = 0
    x = 0
  • Where is the y-intercept of the following graph?
    There's an asymptote there
    On the beach in Tahiti sipping a margarita
    At the origin
    There's a hole there