Asked by Kate

Write an equation that would have a hole at x = 4 and a vertical asympote at x = -2.

My answer was f(x)= (x-4)/(x+2)

If it is not correct can someone please help me solve it and explain it to me? Thanks!
Answered by Scott
a hole is a disruption at a single point
... try [(x - 4) / (x - 4)]
... the division by zero causes the discontinuity, but the equal numerator means no other point is affected

f(x) = (x - 4) / [(x - 4) (x + 2)]
Answered by Kate
Ohhh I see thanks Scott!
Answered by Kate
Sorry I actually have one more question. After solving for your equation the vertical asymptote would actually be 2 and not -2?? So can you still help me create the correct equation
Answered by Kate
Would it be f(x) = (x-4) / (x-4)(x+2)???
Answered by Reiny
Scott was right, the denominator causing the vertical asymptote at x = -2 is
x+2

final answer:
f(x) = (x-4)/( (x-4)(x+2) )
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