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Question

Which function has a graph with a vertical asymptote at   x = 3? Select all that apply .

  1. straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 2 over denominator x squared plus 2 x minus 15 end fraction
  2. straight F left parenthesis straight x right parenthesis equals fraction numerator straight x minus 3 over denominator 12 plus 7 straight x plus straight x squared end fraction
  3. straight F left parenthesis straight x right parenthesis equals fraction numerator x squared minus 9 over denominator x plus 9 end fraction
  4. Non of the above

The correct answer is: straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 2 over denominator x squared plus 2 x minus 15 end fraction


     a)    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

    x2 + 2x - 15= 0
    x2 + 5x -3x - 15= 0
    x(x + 5) – 3(x + 5)
    (x + 5) (x - 3)
    x = -5 and x = 3
    The vertical asymptote of the rational function is x =-5 and x =3
    b)    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

    x2 + 7x + 12= 0
    x2 + 4x + 3x + 12= 0
    x(x + 4) + 3(x + 4)
    (x + 4)(x + 3)
    x = -4 and x = -3
    The vertical asymptote of the rational function is x =-4 and x = -3.
    c)    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

    x + 9 = 0
    x = -9
    Function
    a. straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 2 over denominator x squared plus 2 x minus 15 end fraction   has vertical asymptote at x = 3.

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