A cylindrical can needs to have a volume of 6 cubic inches. A label is to go around the side of the can. The function \(S(r)=\frac{12}{r}\) gives the area of the label in square inches, where \(r\) is the radius of the can in inches.

1. As \(r\) gets closer and closer to 0, what does the behavior of the function tell you about the situation?
2. As \(r\) gets larger and larger, what does the end behavior of the function tell you about the situation?

What is the equation of the vertical asymptote for the graph of the rational function \(g(x) = \frac{6}{x-1}\)?

A geometric sequence \(h\) starts at 16 and has a growth factor of 1.75. Sketch a graph of \(h\) showing the first 5 terms.

Technology required. A 6 oz cylindrical can of tomato paste needs to have a volume of 178 cm³. The current can design uses a radius of 2.75 cm and a height of 7.5 cm. Use graphing technology to find a cylindrical design that would have less surface area so each can uses less metal.

The surface area \(S(r)\), in square units, of a cylinder with a volume of 20 cubic units is a function of its radius \(r\), in units, where \(S(r)=2\pi r^2+\frac{40}{r}\). What is the surface area of a cylinder with a volume of 20 cubic units and a radius of 4 units?