These numbers represent a set of specific values. However, occasionally we are interested in a specific list of numbers like the range for the price to send letters, p = $0.44, $0.61, $0.78, or $0.95. Using inequalities, such as 0 < c ≤ 163, 0 < w ≤ 3.5, and 0 < h ≤ 379 imply that we are interested in all values between the low and high values, including the high values in these examples.
This is one way to describe intervals of input and output values, but is not the only way. In the previous examples, we used inequalities to describe the domain and range of the functions. Since possible prices are from a limited set of values, we can only define the range of this function by listing the possible values. Technically 0 could be included in the domain, but logically it would mean we are mailing nothing, so it doesn’t hurt to leave it out. Since acceptable weights are 3.5 ounces or less, and negative weights don’t make sense, the domain would be 0 < w ≤ 3.5. Suppose we notate Weight by w and Price by p, and set up a function named P, where Price, p is a function of Weight, w. When sending a letter through the United States Postal Service, the price depends upon the weight of the letter, as shown in the table below.
