1. **State the problem:** We need to graph the function $$y = 3(11)^x$$ and understand its behavior. 2. **Formula and rules:** This is an exponential function of the form $$y = a b^x$$ where: - $$a = 3$$ is the initial value (the value when $$x=0$$). - $$b = 11$$ is the base, which is greater than 1, so the function represents exponential growth. - The horizontal asymptote is $$y=0$$ because as $$x \to -\infty$$, $$y \to 0$$. 3. **Evaluate key points:** - When $$x=0$$, $$y = 3 \times 11^0 = 3 \times 1 = 3$$. - When $$x=1$$, $$y = 3 \times 11^1 = 3 \times 11 = 33$$. - When $$x=-1$$, $$y = 3 \times 11^{-1} = 3 \times \frac{1}{11} = \frac{3}{11} \approx 0.27$$. 4. **Behavior explanation:** - As $$x$$ increases, $$11^x$$ grows very fast, so $$y$$ increases steeply. - As $$x$$ decreases, $$11^x$$ approaches 0, so $$y$$ approaches 0 but never reaches it. 5. **Summary:** The graph passes through (0,3), rises steeply for positive $$x$$, and approaches the x-axis (y=0) for negative $$x$$. Final answer: The function $$y = 3(11)^x$$ is an exponential growth curve with horizontal asymptote $$y=0$$, passing through (0,3) and increasing rapidly as $$x$$ increases.