Answer:
Graphs behave differently at various x-intercepts. Sometimes, the graph will cross over the horizontal axis at an intercept. Other times, the graph will touch the horizontal axis and bounce off.
Suppose, for example, we graph the function
\displaystyle f\left(x\right)=\left(x+3\right){\left(x - 2\right)}^{2}{\left(x+1\right)}^{3}f(x)=(x+3)(x−2)
2
(x+1)
3
.
Notice in Figure 7 that the behavior of the function at each of the x-intercepts is different.
Graph of h(x)=x^3+4x^2+x-6.