Corresponding multiplicities

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Section 3.1 (p. 246):
Find the real zeros of the given polynomial and their corresponding multiplicities. Use this information along with a sign chart to provide a rough sketch of the graph of the polynomial. Compare your answer with the result from a graphing utility
According to US Postal regulations, a rectangular shipping box must satisfy the inequality “Length + Girth ≤ 130 inches” for Parcel Post. Let’s assume we have a closed rectangular box with a square face of side length x as drawn below. The length is the longest side and is clearly labeled. The girth is the distance around the box in the other two dimensions so in our case it is the sum of the four sides of the square, 4x.
Assuming that we’ll be mailing a box via Parcel Post where Length + Girth = 130 inches, express the length of the box in terms of x and then express the volume V of the box in terms of x. Volume = V(x) = _________________________________.
Find the dimensions of the box of maximum volume that can be shipped via Parcel Post. X = ___________ , Length = ________________.

Section 4.1 (p. 314): 1,12 (show asymptotes and holes in graphs)
For the given rational function f:

Find the domain of f. Domain: (-∞,0) U (0,∞)
Identify any vertical asymptotes of the graph of y = f(x).
Vertical Asymptotes: x = 0
Identify any holes in the graph. Hole locations: No holes
Find the horizontal asymptote, if it exists. Horizontal Asymptotes: y = 0
Find the slant asymptote, if it exists. Slant Asymptotes: No slant asymptotes
Graph the function using a graphing utility to help you and describe the behavior near the asymptotes.

Behavior near the asymptotes:
As x approaches 0, y becomes large (vertical asymptote)
As become very large, y approaches 0 (horizontal asymptote)

Directions: Find all real solutions. Be sure to check for extraneous solutions. Select the correct answer.

Working together, Daniel and Donnie can clean the llama pen in 45 minutes. On his own,
Daniel can clean the pen in an hour. How long does it take Donnie to clean the llama pen on
his own? Select the correct answer.
1 hour b) 2 hours c) 3 hours d) None of these.