Question

Graph the rational functions. Include the graphs and equations of the asymptotes and dominant terms. \frac{x+3}{x+2}

Rational functions
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asked 2021-05-02
Graph the rational functions. Include the graphs and equations of the asymptotes and dominant terms. \(\displaystyle{\frac{{{x}+{3}}}{{{x}+{2}}}}\)

Answers (1)

2021-05-03
[Graph]
\(\displaystyle{\frac{{{x}+{3}}}{{{x}+{2}}}}={\frac{{{x}}}{{{x}+{2}}}}+{\frac{{{3}}}{{{x}+{2}}}}\). It has a vertical asymptote at x=-2. \(\displaystyle{\frac{{{3}}}{{{x}+{2}}}}\) is dominant near the asymptote, and \(\displaystyle{\frac{{{x}}}{{{x}+{2}}}}\) is dominant as x goes to \(\displaystyle\infty\) or \(\displaystyle-\infty\). (It has the same horizontal asymptote, y=1.
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