1. **Problem statement:** Find the domain and range of the function $$y = (x + 1)(x - 3)$$. 2. **Recall the domain and range definitions:** - The **domain** is the set of all possible input values ($x$) for which the function is defined. - The **range** is the set of all possible output values ($y$) the function can take. 3. **Analyze the function:** The function is a quadratic polynomial, which is defined for all real numbers. 4. **Domain:** Since there are no restrictions like division by zero or square roots of negative numbers, the domain is all real numbers. 5. **Range:** Rewrite the function in standard form: $$y = (x + 1)(x - 3) = x^2 - 3x + x - 3 = x^2 - 2x - 3$$ 6. **Find the vertex to determine the range:** The vertex of a parabola $y = ax^2 + bx + c$ is at $$x = -\frac{b}{2a}$$. Here, $a = 1$, $b = -2$, so $$x = -\frac{-2}{2 \times 1} = 1$$ 7. **Calculate the vertex's $y$ value:** $$y = (1)^2 - 2(1) - 3 = 1 - 2 - 3 = -4$$ 8. **Since $a = 1 > 0$, the parabola opens upwards, so the minimum value of $y$ is $-4$.** 9. **Therefore, the range is:** $$y \geq -4$$ 10. **Summary:** - Domain: $$\mathbb{R}$$ (all real numbers) - Range: $$[-4, \infty)$$