121616949-math.28 - 14 Chapter 1 Analytic Geometry 16 A can...

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14 Chapter 1 Analytic Geometry 16. A can in the shape of a cylinder is to be made to hold a volume of one liter (1000 cubic centimeters). The manufacturer wants to use the least possible material for the can. Write the surface area of the can (total of the top, bottom, and side) as a function of the radius r of the can; find the domain of the function. Many functions in applications are built up from simple functions by inserting constants in various places. It is important to understand the effect such constants have on the appearance of the graph. Horizontal shifts. If you replace x by x - C everywhere it occurs in the formula for f ( x ) , then the graph shifts over C to the right. (If C is negative, then this means that the graph shifts over | C | to the left.) For example, the graph of y = ( x - 2) 2 is the x 2 -parabola shifted over to have its vertex at the point 2 on the x -axis. The graph of y = ( x + 1) 2 is the same parabola shifted over to the left so as to have its vertex at - 1 on the x -axis.
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