1. **Problem Statement:** Analyze the function $$y = 8 \cdot \left(\frac{1}{4}\right)^x$$ to determine its domain, range, y-intercept, and asymptote. 2. **Formula and Rules:** This is an exponential decay function of the form $$y = a \cdot b^x$$ where $$a = 8$$ and $$b = \frac{1}{4}$$ (with $$0 < b < 1$$ indicating decay). 3. **Domain:** The domain of any exponential function $$y = a \cdot b^x$$ is all real numbers, so $$\text{Domain} = (-\infty, \infty)$$. 4. **Range:** Since $$b^x > 0$$ for all real $$x$$ and $$a = 8 > 0$$, the function values are always positive. The function approaches zero but never reaches it, so $$\text{Range} = (0, \infty)$$. 5. **Y-intercept:** The y-intercept occurs at $$x=0$$: $$y = 8 \cdot \left(\frac{1}{4}\right)^0 = 8 \cdot 1 = 8$$ So, the y-intercept is $$8$$. 6. **Asymptote:** As $$x \to \infty$$, $$\left(\frac{1}{4}\right)^x \to 0$$, so $$y \to 0$$. The horizontal asymptote is $$y = 0$$. **Final answers:** - Domain: $$(-\infty, \infty)$$ - Range: $$(0, \infty)$$ - Y-intercept: $$8$$ - Asymptote: $$y = 0$$