Finding Domain and Range from a Graph of Oil Production

Find the domain and range of the function $f$ whose graph is shown in Figure 11.

Figure 11 (credit: modification of work by the U.S. Energy Information Administration)4

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The input quantity along the horizontal axis is “years,” which we represent with the variable $t$ for time. The output quantity is “thousands of barrels of oil per day,” which we represent with the variable $b$ for barrels. The graph may continue to the left and right beyond what is viewed, but based on the portion of the graph that is visible, we can determine the domain as $1973 \leq t \leq 2008$ and the range as approximately $180 \leq b \leq 2010.$

In interval notation, the domain is [1973, 2008], and the range is about [180, 2010]. For the domain and the range, we approximate the smallest and largest values since they do not fall exactly on the grid lines.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given Figure 12, identify the domain and range using interval notation.

Figure 12

How did it go?