Construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2. Explain how you determined your answer.

Reggie

Reggie

Answered question

2021-02-11

Construct a rational function that has a vertical asymptote at x=3 and a removable discontinuity at x=2.
Explain how you determined your answer.

Answer & Explanation

doplovif

doplovif

Skilled2021-02-12Added 71 answers

Since x=3 is a vertical asymptote, then x3 is a factor in the denominator. Given that  x=2 has a removable discontinuity, then x+2 is a common factor in the numerator and denominator. So, here is a potential rational function:
f(x)=x+2(x3)(x+2) 
or 
f(x)=x+2x2x6

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