(a) The V-shaped graph has slopes −3 and 3, and intercepts (0,7), (7/3,0):

(b) Every line \(y=k(x-4)\) passes through (4,0), to the right of the vertex. A negative slope between the left-branch slope \(-3\) and 0 crosses both branches. At \(k=-3\) it is parallel to the left branch, and at \(k=0\) there is only the vertex. For \(k>0\), or \(k<-3\), at most one intersection occurs. Hence \(\boxed{-3<k<0}\).