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

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Answer 1 · 2015-02-26T15:12:45

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

How do I identify the x-intercept(s) and vertical asymptote(s): y=5x2−1y=5/(x^2-1)?