1. **State the problem:** We are given the function $$y = - (0.8)^x - 5$$ and want to understand its behavior and graph shape. 2. **Formula and rules:** This is an exponential function of the form $$y = -a^x + c$$ where $$a = 0.8$$ and $$c = -5$$. - Since $$0 < a < 1$$, $$a^x$$ represents exponential decay. - The negative sign in front reflects the graph vertically. - The $$-5$$ shifts the graph down by 5 units. 3. **Analyze the function:** - The base $$0.8$$ means the function decreases as $$x$$ increases. - The negative sign flips the decay curve upside down. - The vertical shift moves the entire graph down. 4. **Key points:** - When $$x=0$$, $$y = - (0.8)^0 - 5 = -1 - 5 = -6$$. - As $$x \to \infty$$, $$ (0.8)^x \to 0$$, so $$y \to -0 - 5 = -5$$ (horizontal asymptote). - As $$x \to -\infty$$, $$ (0.8)^x \to \infty$$, so $$y \to -\infty - 5 = -\infty$$. 5. **Summary:** The graph is a vertically reflected exponential decay curve shifted down 5 units, with horizontal asymptote at $$y = -5$$ and passing through $$(-6)$$ at $$x=0$$. Final answer: The function $$y = - (0.8)^x - 5$$ is a vertically reflected exponential decay shifted down by 5 units with horizontal asymptote $$y = -5$$ and passes through point $$(0,-6)$$.