Analyze the graph of cubic function \( f(x)=x^{3} \) and the transformed function \( g(x) \); then determine by how much the graph of \( f(x) \) shifts horizontally to the right. (1 point) The function \( f(x) \) shifts horizontally \( \square \) units to the right.

To determine by how much the graph of \( f(x) = x^3 \) shifts horizontally to the right when transformed into \( g(x) \), we need to look at the form of the transformed function. If \( g(x) \) takes the form \( g(x) = (x - h)^3 \), the graph of \( f(x) \) shifts \( h \) units to the right if \( h \) is positive. For example, if \( g(x) = (x - 2)^3 \), the graph of \( f(x) \) shifts horizontally \( 2 \) units to the right. However, if \( g(x) \) has a different form (like \( g(x) = (x + 3)^3 \)), it would shift \( 3 \) units to the left instead. So, to fill in the blank, if \( g(x) = (x - h)^3 \), the function \( f(x) \) shifts horizontally \( h \) units to the right. If you provide the specific form of \( g(x) \), I can give you the exact number of units. The function \( f(x) \) shifts horizontally \( \square \) units to the right.