Consider the polynomial function. f(x)=x(x−2)^3(x+5)^2 .
Which statements correctly describes the behavior of the graph of the function at its zeros?
- The graph of the function crosses through the x-axis at 2 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 0 and crosses straight through the x-axis at 5.
- The graph of the function crosses through the x-axis at 2 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at −5 and crosses straight through the x-axis at 0.
- The graph of the function crosses through the x-axis at −2 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 0 and crosses straight through the x-axis at 5.
- The graph of the function crosses through the x-axis at −5 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 2 and crosses straight through the x-axis at 0.
