Question 3 of 10 This quiz: 100 point(s) possible This question: 10 point(s) possible Describe verbally the transformations that can be used to obtain the graph of g from the graph of f \[ g(x)=7^{x-6} \cdot f(x)=T^{x} \]

To transform the graph of \( f(x) \) into \( g(x) = 7^{x-6} \cdot f(x) \), you will first apply a horizontal shift. The term \( x-6 \) indicates that the graph of \( f(x) \) will be shifted 6 units to the right. Next, the exponential term \( 7^{x} \) introduces a vertical stretch since it scales the function by 7. The combination of these transformations results in a graph that is not only displaced but also stretched vertically, giving it a more pronounced shape. In practical terms, to sketch \( g(x) = 7^{x-6} \cdot f(x) \), first plot the graph of \( f(x) \), then move every point 6 units to the right, and finally stretch the graph vertically by a factor of 7. This will significantly increase the values of \( g(x) \) for each corresponding \( x \), making the peaks higher, and troughs dip lower, creating a distinct visual variation from \( f(x) \) that reflects the dual transformations applied.