1. **Stating the problem:** We need to graph the function $$y = -4(10^x)$$ and understand its behavior. 2. **Understanding the function:** This is an exponential function of the form $$y = a \cdot b^x$$ where $$a = -4$$ and $$b = 10$$. 3. **Key properties of exponential functions:** - The base $$b = 10$$ is greater than 1, so $$10^x$$ is an increasing exponential function. - The coefficient $$a = -4$$ is negative, which reflects the graph across the x-axis and scales it by 4. 4. **Horizontal asymptote:** For $$y = a \cdot b^x$$ with $$b > 0$$, the horizontal asymptote is $$y = 0$$. Since $$a$$ is negative, the graph approaches 0 from below as $$x \to -\infty$$. 5. **Evaluating key points:** - At $$x=0$$, $$y = -4(10^0) = -4(1) = -4$$. - At $$x=1$$, $$y = -4(10^1) = -4(10) = -40$$. - At $$x=-1$$, $$y = -4(10^{-1}) = -4 \times \frac{1}{10} = -0.4$$. 6. **Behavior summary:** - As $$x$$ increases, $$10^x$$ grows rapidly, so $$y$$ becomes very large negative. - As $$x$$ decreases, $$10^x$$ approaches 0, so $$y$$ approaches 0 from below. 7. **Graph shape:** - The graph is a decreasing curve starting near 0 (from below) on the left, - Crossing the y-axis at $$-4$$, - And dropping steeply downward as $$x$$ increases. 8. **Formula recap:** $$y = -4(10^x)$$ This explains the graph described: a decreasing exponential curve with horizontal asymptote $$y=0$$, crossing the y-axis at $$-4$$, approaching 0 from below as $$x$$ goes left, and dropping rapidly downward as $$x$$ increases. **Final answer:** The graph of $$y = -4(10^x)$$ is a decreasing exponential curve reflected below the x-axis with horizontal asymptote $$y=0$$ and y-intercept at $$-4$$.