how to find domain of a graph

Some other style to identify the domain and range of functions is by using graphs. Because the domain refers to the ready of possible input values, the domain of a graph consists of all the input values shown on the x-centrality. The range is the set of possible output values, which are shown on the y-axis. Proceed in listen that if the graph continues across the portion of the graph we tin can run across, the domain and range may be greater than the visible values. Come across Figure 6.

Graph of a polynomial that shows the x-axis is the domain and the y-axis is the range

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We can discover that the graph extends horizontally from [latex]-5[/latex] to the right without bound, so the domain is [latex]\left[-v,\infty \right)[/latex]. The vertical extent of the graph is all range values [latex]5[/latex] and below, and so the range is [latex]\left(\mathrm{-\infty },v\correct][/latex]. Notation that the domain and range are ever written from smaller to larger values, or from left to right for domain, and from the lesser of the graph to the elevation of the graph for range.

Example 6: Finding Domain and Range from a Graph

Find the domain and range of the function [latex]f[/latex] whose graph is shown in Figure seven.

Graph of a function from (-3, 1].

Effigy seven

Solution

Nosotros can observe that the horizontal extent of the graph is –three to 1, so the domain of [latex]f[/latex] is [latex]\left(-3,1\right][/latex].

This graph has three lines, two straight and one that is curvy. It shows that the domain starts at -3 (not including -3) all the way to 1. The range shows from -4 to 0.

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The vertical extent of the graph is 0 to –4, so the range is [latex]\left[-4,0\right][/latex].

Example 7: Finding Domain and Range from a Graph of Oil Production

Notice the domain and range of the office [latex]f[/latex] whose graph is shown in Figure nine.

Solution

The input quantity along the horizontal axis is "years," which we stand for with the variable [latex]t[/latex] for time. The output quantity is "thousands of barrels of oil per day," which we represent with the variable [latex]b[/latex] for barrels. The graph may keep to the left and right across what is viewed, simply based on the portion of the graph that is visible, we can determine the domain as [latex]1973\le t\le 2008[/latex] and the range as approximately [latex]180\le b\le 2010[/latex].

In interval note, the domain is [1973, 2008], and the range is most [180, 2010]. For the domain and the range, nosotros approximate the smallest and largest values since they exercise non fall exactly on the grid lines.