1. The problem asks to compare the graph of the second function $$y=\frac{1}{7}4^{-2x-10}-3$$ to the graph of the first function $$y=4^x$$. 2. Start with the first function $$y=4^x$$, which is an exponential growth function. It increases rapidly as $$x$$ increases. 3. Analyze the second function step-by-step: - The base is still 4, but the exponent is $$-2x-10$$ instead of $$x$$. - The negative sign in front of $$2x$$ reflects the graph across the y-axis. - The factor 2 compresses the graph horizontally by a factor of $$\frac{1}{2}$$. - The $$-10$$ inside the exponent shifts the graph horizontally to the right by 10 units (because $$-2x-10 = -2(x+5)$$). - The coefficient $$\frac{1}{7}$$ vertically compresses the graph by a factor of $$\frac{1}{7}$$. - The $$-3$$ outside shifts the graph downward by 3 units. 4. Summarizing the transformations from $$y=4^x$$ to $$y=\frac{1}{7}4^{-2x-10}-3$$: - Reflection about the y-axis. - Horizontal compression by factor 2. - Horizontal shift right by 5 units. - Vertical compression by factor $$\frac{1}{7}$$. - Vertical shift downward by 3 units. 5. These transformations change the shape and position of the graph significantly compared to the original exponential growth curve. Final answer: The second function's graph is a reflected, horizontally compressed, right-shifted, vertically compressed, and downward-shifted version of the first function's graph.