Limits and Continuity · Medium problem

A continuous function $f$ on $[0,4]$ satisfies $f(0)=2$ and $f(4)=5$. Let $g(x)=f(x)-(3x-1)$. Compute $g(0)\cdot g(4)$, and use its sign to say whether the graph of $f$ must cross the line $y=3x-1$ somewhere in $(0,4)$.