Chapter 4.2, Problem 61ES

In each part: (i) Make a conjecture about the behavior of the graph in the vicinity of its x-intercepts. (ii) Make a rough sketch of the graph based on your conjecture and the limits of the polynomial as $x\to +\infty$ and as $x\to -\infty$ . (iii) Compare your sketch to the graph generated with a graphing utility.

(a) $y=x\left(x-1\right)\left(x+1\right)$

(b) $y=x^2{\left(x-1\right)}^2{\left(x+1\right)}^2$

(c) $y=x^2{\left(x-1\right)}^2{\left(x+1\right)}^3$

(d) $y=x{\left(x-1\right)}^5{\left(x+1\right)}^4$