How do I identify the x-intercept(s) and vertical asymptote(s): y=(x^3+27)/(3x^2+x)?
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=(x^3+27)/(3x^2+x)
In order for this fraction to equal 0, the numerator of the fraction must equal 0 (remember: denominator = 0 -> undefined)
0=(x^3+27)
x^3=-27
x=-3
So the x-intercept: (-3,0) -
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=(x^3+27)/(3x^2+x) is already simplified
Undefined when denominator = 0:(3x^2+x)=0
x(3x+1)=0
x=0, 3x+1=0
Vertical asymptotes:x=0, x=-1/3