To analyze the effect of replacing the function \( f(x) = x^3 \) with \( f(x) = (bx)^3 \) where \( b > 1 \), we can rewrite the new function as:
\[ f(x) = b^3 x^3 \]
This shows that the transformation involves a scaling of the \( x \)-values. When \( b > 1 \), the operation \( bx \) compresses the input \( x \) because it's effectively increasing the rate at which \( x \) values reach their larger output values.
To see how this affects the graph:
- For a given output \( y \), the new function yields the same \( y \)-value, but for a smaller input value of \( x \), due to the multiplication by \( b \) (which is greater than 1). This means that the graph is compressed horizontally.
In summary:
- The transformation \( f(x) = (bx)^3 \) for \( b > 1 \) causes the graph to be horizontally compressed.
Thus, the correct option that describes the effect is:
the graph is horizontally compressed.