How do I identify the xintercept(s) and vertical asymptote(s): #y=5/(x^21)#?
1 Answer
Feb 26, 2015

To identify the xintercepts, you want to ask yourself: "where does the graph hit the xaxis, aka: what is x when y=0?"
So let y = 0 and solve for x:
#0 = 5/(x^21)#
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 xintercept 
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^21)# is already simplified
Undefined when denominator = 0:#(x^21) = 0#
#(x+1)(x1)=1#
VA:#x=1# ,#x=1#