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2 Functions > 2.8 Building a Function from Words
2.8 Building a Function from Words
Introduction In calculus there will be several instances when you will be expected to translate the words that describe a problem into mathematical symbols and then set up or construct either an equation or a function.
In this section we focus on problems that involve functions. We begin with a verbal description about the product of two numbers.
EXAMPLE 1 Product of Two Numbers
The sum of two nonnegative numbers is 15. Express the product of one and the square of the other as a function of one of the numbers.
Solution We first represent the two numbers by the symbols x and y and recall that “nonnegative” means that x = 0 and y = 0. The first sentence then says that x + y = 15; this is not the function we are seeking. The second sentence describes the function we want; it is called “the product.” Let’s denote “the product” by the symbol P. Now P is the product of one of the numbers, say, x and the square of the other, that is, y2:
