\( f(x)=x^{2} \) \( g(x)=(x-6)^{2} \) We can think of \( g \) as a translated (shifted) version of \( f \). Complete the description of the transformation. Use nonnegative numbers. To get the function \( g \), shift \( f \) up/down/left/right

To get the function \( g \), shift \( f \) right by 6 units. This transformation of the function moves every point on the graph of \( f(x) = x^2 \) horizontally to the right, effectively creating the new function \( g(x) = (x-6)^2 \). So while \( f \) has its vertex at the origin (0,0), \( g \) has its vertex shifted to the right, situated at the point (6,0) on the graph. Now, if we combine that with the knowledge of how quadratic functions behave, we can see that shifting a function horizontally affects the input (the x-values) directly, while the output (the y-values) remains unchanged apart from the vertical height. This means our transformation preserves the parabolic shape but adjusts the location for visualizing the function.