How do I identify the x-intercept(s) and vertical asymptote(s): #y=5/(x^2-1)#?
1 Answer
Feb 26, 2015
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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 -
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#