Question

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

Answer 1

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`