1. **State the problem:** Graph the function $$y=\left(\frac{1}{2}\right)^{x-1} - 10$$ using the given table of values and identify the asymptote. 2. **Formula and rules:** The function is an exponential decay of the form $$y=a^{x-h}+k$$ where $$a=\frac{1}{2}$$ (between 0 and 1, so decay), $$h=1$$ (horizontal shift), and $$k=-10$$ (vertical shift). 3. **Asymptote:** The horizontal asymptote is $$y=k=-10$$ because as $$x\to\infty$$, $$\left(\frac{1}{2}\right)^{x-1}\to 0$$, so $$y\to -10$$. 4. **Intermediate work:** Calculate a few values to confirm the table: $$y=\left(\frac{1}{2}\right)^{x-1} - 10$$ For $$x=-10$$: $$y=\left(\frac{1}{2}\right)^{-11} - 10 = 2^{11} - 10 = 2048 - 10 = 2038$$ Matches the table. For $$x=1$$: $$y=\left(\frac{1}{2}\right)^{0} - 10 = 1 - 10 = -9$$ Matches the table. For $$x=10$$: $$y=\left(\frac{1}{2}\right)^{9} - 10 = \frac{1}{512} - 10 \approx -9.9980469$$ Matches the table. 5. **Graph shape explanation:** The graph is an exponential decay curve starting very high for large negative $$x$$ values, passing through the points given, and approaching the horizontal asymptote $$y=-10$$ from above as $$x$$ increases. **Final answer:** The function $$y=\left(\frac{1}{2}\right)^{x-1} - 10$$ has a horizontal asymptote at $$y=-10$$ and its graph is an exponential decay curve passing through the given points and approaching $$y=-10$$ from above as $$x\to\infty$$.