![]() ![]() The output is “thousands of barrels of oil per day”, which we might notate with the variable b, for barrels. In the graph above, the input quantity along the horizontal axis appears to be “year”, which we could notate with the variable y. Likewise, since range is the set of possible output values, the range of a graph we can see from the possible values along the vertical axis of the graph.īe careful – if the graph continues beyond the window on which we can see the graph, the domain and range might be larger than the values we can see. Remember that input values are almost always shown along the horizontal axis of the graph. ![]() Since domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the graph. We can also talk about domain and range based on graphs. Remember when writing or reading interval notation: using a square bracket [ means the start value is included in the set using a parenthesis ( means the start value is not included in the set. 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. ![]()
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