relate the domain of a function to its graph

Another fashio to identify the domain and range of functions is by using graphs. Because the domain refers to the set of feasible stimulation values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of affirmable output values, which are shown on the y-bloc. Keep in listen that if the graph continues beyond the portion of the graph we can see, the orbit and range may be greater than the visible values. See Figure 6.

Figure 6

We tooshie respect that the graphical record extends horizontally from [latex]-5[/latex] to the honourable without bound, so the domain is [latex]\left over[-5,\infty \right)[/latex paint]. The vertical extent of the graph is complete range values [latex paint]5[/latex] and below, so the range is [latex]\left(\mathrm{-\infty },5\word-perfect][/latex]. Note that the domain and rank are ever graphical from littler to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range.

Exercise 6: Finding Domain and Range from a Graph

Find the domain and compass of the function [latex]f[/latex] whose graphical record is shown in Figure 7.

Digit 7

Solution

We can celebrate that the horizontal extent of the graph is –3 to 1, so the domain of [latex]f[/rubber-base paint] is [latex]\left-hand(-3,1\right][/latex].

Figure 8

The vertical extent of the graph is 0 to –4, so the range is [latex]\socialistic[-4,0\rightfulness][/rubber-base paint].

Exemplar 7: Finding Domain and Range from a Graphical record of Drilling

Find the domain and range of the function [latex]f[/latex] whose graph is shown in Figure 9.

Resolution

The input quantity on the horizontal axis is "years," which we represent with the variable [latex]t[/latex paint] for time. The output quantity is "thousands of barrels of embrocate per day," which we represent with the variable [latex]b[/latex] for barrels. The graph may continue to the left and right on the far side what is viewed, but founded on the portion of the graphical record that is visible, we derriere determine the domain as [latex]1973\LE t\le 2008[/latex] and the kitchen range as approximately [latex paint]180\LE b\LE 2010[/latex].

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

Try It 6

Given the graph in Build 10, key the domain and roll using interval notation.

Figure 10

Solution

Q & A

Can a function's domain and mountain chain represent the comparable?

Yes. For instance, the domain and range of the block root office are both the set of all real Numbers.

relate the domain of a function to its graph

Source: https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/find-domain-and-range-from-graphs/#:~:text=Another%20way%20to%20identify%20the,shown%20on%20the%20y%2Daxis.

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