1. **Problem Statement:** Determine if the graph of the line passing through points $(-10, 10)$ and $(10, -10)$ defines a function, and find its domain and range. 2. **Check if the graph defines a function:** A graph defines a function if for every $x$-value there is exactly one $y$-value. This is the vertical line test. 3. **Apply the vertical line test:** The line passes through $(-10, 10)$ and $(10, -10)$ and extends beyond. It is a straight line with no vertical segments, so every vertical line intersects it at exactly one point. 4. **Conclusion on function:** Since the line passes the vertical line test, it defines a function. 5. **Find the equation of the line:** Use the slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-10 - 10}{10 - (-10)} = \frac{-20}{20} = -1$$ 6. Use point-slope form with point $(-10, 10)$: $$y - 10 = -1(x - (-10))$$ $$y - 10 = -1(x + 10)$$ $$y - 10 = -x - 10$$ $$y = -x - 10 + 10$$ $$y = -x$$ 7. **Domain:** The line extends infinitely in both directions along the $x$-axis, so the domain is all real numbers: $$\text{Domain} = (-\infty, \infty)$$ 8. **Range:** Since $y = -x$, as $x$ takes all real values, $y$ also takes all real values: $$\text{Range} = (-\infty, \infty)$$