How do I identify the x-intercept(s) and vertical asymptote(s): y=5/(x^2-1)?

1 Answer
Feb 26, 2015
  1. To identify the x-intercepts, you want to ask yourself: "where does the graph hit the x-axis, aka: what is x when y=0?"
    So let y = 0 and solve for x:
    0 = 5/(x^2-1)
    In order for this fraction to equal 0, the numerator of the fraction must equal 0 (remember: denominator = 0 -> undefined)
    0 = 5 -> never
    So we have no x-intercept

  2. To identify the vertical asymptotes, we first try and simplify the function as much as possible and then look at where it is undefined
    y = 5/(x^2-1) is already simplified
    Undefined when denominator = 0: (x^2-1) = 0
    (x+1)(x-1)=1
    VA: x=1, x=-1