the points (-6,0)(-2,0)(1,0)(3,0) all exist in the graph which is only correct for the second graph to make your self even more sure since the zeros are given and it ia a polynomial you can figure out the facrored form which will yield f(x)=(x+6)(x+2)(x-1)(x-3) conducting a simple sign test ------------------------------------------' there will be 4 critical values -6 -2 1 3 before -6 the sign of f(x) -*-*-*-= + after -6 and before -2 the sign of f(x) +*-*-*-=- after -2 and before 1 the sign of f(x) +*+*-*-=+ after 1 and before 3 the sign of f(x) +*+*+*-=- after 3 the sign of f(x) +*+*+*+=+ which only fits the upper right graph