Answer
$y=1-{27}x^3$
Work Step by Step
Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f\left({c}x\right)$ by horizontally compressing the graph of $y=f(x)$ by a factor of $c$.
Hence to horizontally compress the graph of $y=1-x^3$ by a factor of 3, we replace each occurrence of $x$ in this equation by ${3}x$ obtaining the equation $$y=1-\left({3}x\right)^3,$$ or equivalently, $$y=1-{27}x^3.$$
