1. **State the problem:** We want to describe the long run behavior of the function $$f(x) = 2(2)^x + 3$$ as $$x \to -\infty$$ and $$x \to \infty$$. 2. **Recall the properties of exponential functions:** For the base $$a > 1$$, $$a^x$$ approaches 0 as $$x \to -\infty$$ and grows without bound as $$x \to \infty$$. 3. **Analyze the behavior as $$x \to -\infty$$:** Since $$2^x \to 0$$ as $$x \to -\infty$$, $$f(x) = 2(2)^x + 3 \to 2 \cdot 0 + 3 = 3$$. 4. **Analyze the behavior as $$x \to \infty$$:** Since $$2^x \to \infty$$ as $$x \to \infty$$, $$f(x) = 2(2)^x + 3 \to 2 \cdot \infty + 3 = \infty$$. 5. **Summary:** - As $$x \to -\infty$$, $$f(x) \to 3$$. - As $$x \to \infty$$, $$f(x) \to \infty$$. This means the graph approaches the horizontal asymptote $$y=3$$ on the left and increases without bound on the right.