1. **State the problem:** We are given the rational function $$y = \frac{x + 4}{x - 2}$$ and want to understand its behavior and graph. 2. **Identify key features:** - The function is undefined where the denominator is zero, so vertical asymptote at $$x = 2$$. - For large $$|x|$$, the function behaves like $$\frac{x}{x} = 1$$, so horizontal asymptote at $$y = 1$$. 3. **Find intercepts:** - **x-intercept:** Set numerator to zero: $$x + 4 = 0 \Rightarrow x = -4$$, so intercept at $$(-4, 0)$$. - **y-intercept:** Set $$x=0$$: $$y = \frac{0 + 4}{0 - 2} = \frac{4}{-2} = -2$$, so intercept at $$(0, -2)$$. 4. **Analyze behavior near vertical asymptote:** - As $$x \to 2^-$$, denominator approaches zero from negative side, numerator $$2 + 4 = 6$$ positive, so $$y \to -\infty$$. - As $$x \to 2^+$$, denominator approaches zero from positive side, numerator positive, so $$y \to +\infty$$. 5. **Summary:** - Vertical asymptote at $$x=2$$. - Horizontal asymptote at $$y=1$$. - x-intercept at $$(-4,0)$$. - y-intercept at $$(0,-2)$$. This explains the graph's key features and behavior.