1. **Stating the problem:** We have two functions: $$y=2x - m^2 - 2$$ and $$y=-2x - m^2 - 2$$. We need to analyze their range, domain, vertex, and maximum value. 2. **Domain:** Both functions are linear in $x$ (no denominators or square roots involving $x$), so their domain is all real numbers, $$\mathbb{R}$$. 3. **Range:** Since both are linear functions with slope $2$ and $-2$ respectively, their range is also all real numbers, $$\mathbb{R}$$. 4. **Vertex:** Linear functions do not have vertices because they are straight lines, not parabolas. So, they do not have a vertex, maximum, or minimum. 5. **Maximum at $y=-2$?:** Since these are linear functions with nonzero slopes, they do not have a maximum or minimum value. The value $-2$ appears as part of the constant term but is not a maximum. **Summary:** - A. Same range: True (both have range $$\mathbb{R}$$) - B. Same domain: True (both have domain $$\mathbb{R}$$) - C. Different vertex: False (no vertices) - D. Maximum at $y=-2$: False (no maximum) **Final answers:** A and B are true; C and D are false.