6. The five graphs below have equal scales on the x and y axes. Which one could be the graph of y = 3x4 4x3 ?

 

 

A

B

C

D

E

 

 

 Solution: The answer is D

 

By the leading coefficient test we can disregard graph A. Since the leading coefficient is positive and the degree of y is even, then the graph of y rises to the left and right. Furthermore, factoring y yields,

 

 

The factor x3 results in a repeated zero of multiplicity 3 which accounts for three of the four real zeros of y and since the multiplicity is odd then it must cross the x-axis at x = 0. Which allows us to disregard graph B and E. The factor (3x 4) results in a positive zero for y and hence we can disregard graph C. So, graph D, must be the graph of y.