1. The problem is to graph the function $$d(x) = 7|x - 7| - 8$$. 2. This function involves an absolute value expression. The absolute value function $$|x|$$ outputs the distance of $$x$$ from zero, always non-negative. 3. The function $$d(x) = 7|x - 7| - 8$$ can be seen as a vertical stretch by 7, a horizontal shift right by 7 units, and a vertical shift down by 8 units of the basic absolute value function $$|x|$$. 4. To understand the shape, consider two cases: - When $$x \geq 7$$, $$|x - 7| = x - 7$$, so $$d(x) = 7(x - 7) - 8 = 7x - 49 - 8 = 7x - 57$$. - When $$x < 7$$, $$|x - 7| = 7 - x$$, so $$d(x) = 7(7 - x) - 8 = 49 - 7x - 8 = 41 - 7x$$. 5. The vertex of the graph is at $$x = 7$$, where $$d(7) = 7|7 - 7| - 8 = 0 - 8 = -8$$. 6. The graph is a "V" shape with vertex at $$(7, -8)$$, opening upwards with slopes 7 and -7 on either side. Final answer: The function $$d(x) = 7|x - 7| - 8$$ is a vertically stretched and shifted absolute value graph with vertex at $$(7, -8)$$.