Question

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

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