1. **State the problem:** We are given the function $$P(x) = \frac{3000x - 160000}{x + 300}$$ and want to analyze it. 2. **Formula and rules:** This is a rational function where the numerator is $$3000x - 160000$$ and the denominator is $$x + 300$$. Important rules: - The function is undefined where the denominator is zero. - Simplify the expression if possible. 3. **Find domain restrictions:** Set denominator equal to zero: $$x + 300 = 0 \implies x = -300$$ So, $$P(x)$$ is undefined at $$x = -300$$. 4. **Simplify the function:** Factor numerator if possible: $$3000x - 160000 = 1000(3x - 160)$$ No common factor with denominator $$x + 300$$, so no simplification. 5. **Find intercepts:** - **x-intercept:** Set numerator to zero: $$3000x - 160000 = 0 \implies 3000x = 160000 \implies x = \frac{160000}{3000} = \frac{1600}{30} = \frac{160}{3} \approx 53.33$$ - **y-intercept:** Set $$x=0$$: $$P(0) = \frac{3000 \cdot 0 - 160000}{0 + 300} = \frac{-160000}{300} = -\frac{160000}{300} = -\frac{1600}{3} \approx -533.33$$ 6. **Behavior near vertical asymptote:** At $$x = -300$$, the function tends to infinity or negative infinity depending on the side. 7. **Horizontal asymptote:** Since degrees of numerator and denominator are equal (both degree 1), horizontal asymptote is ratio of leading coefficients: $$y = \frac{3000}{1} = 3000$$ **Final answer:** The function $$P(x) = \frac{3000x - 160000}{x + 300}$$ has domain $$x \neq -300$$, x-intercept at $$x = \frac{160}{3}$$, y-intercept at $$y = -\frac{1600}{3}$$, vertical asymptote at $$x = -300$$, and horizontal asymptote at $$y = 3000$$.