Question

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.

Rational functions
ANSWERED
asked 2021-05-16
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.

Answers (1)

2021-05-17
Since x=3 is a vertical asymptote, then x−3 is a factor in the denominator. Since there is a removable discontinuity at x=−2, then x+2 is a common factor in the numerator and denominator. So, a possible rational function is:
\(\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}+{2}}}{{{\left({x}-{3}\right)}{\left({x}+{2}\right)}}}\)
or
\(\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}+{2}}}{{{x}^{{2}}-{x}-{6}}}\)
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