Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 351: 4

$C$.

Step 1. For $y=-x^3+9x^2-27x+17$, we have $n=3, a_3=-1$, thus the end behaviors are fall to the right and rise to the left. The maximum number of real zeros is $3$ Step 2. Based on the graphs of C and D, although they both fit the end behaviors, graph $D$ contains too many real zeros. Thus the answer is $C$.