微积分网课代修|预备微积分代写precalculus辅导|MATH165 Finding Domain and Range from Graphs

微积分网课代修|预备微积分代写precalculus辅导|MATH165 Finding Domain and Range from Graphs

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微积分网课代修|预备微积分代写precalculus辅导|MATH165 Finding Domain and Range from Graphs

微积分网课代修|预备微积分代写precalculus辅导|Finding Domain and Range from Graphs

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the $x$-axis. The range is the set of possible output values, which are shown on the $y$-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values. See Figure 8 .

We can observe that the graph extends horizontally from $-5$ to the right without bound, so the domain is $[-5, \infty)$. The vertical extent of the graph is all range values 5 and below, so the range is $(-\infty, 5]$. Note that the domain and range are always written from smaller 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.

微积分网课代修|预备微积分代写precalculus辅导|Finding Domain and Range from a Graph

Find the domain and range of the function $f$ whose graph is shown in Figure 9 .

Solution We can observe that the horizontal extent of the graph is $-3$ to 1 , so the domain of $f$ is $(-3,1]$.
The vertical extent of the graph is 0 to $-4$, so the range is $[-4,0]$. See Figure 10 .

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 $180 \leq b \leq 2010$.

微积分网课代修|预备微积分代写precalculus辅导|MATH165 Finding Domain and Range from Graphs

微积分网课代修|预备微积分代写precalculus辅导| Finding Domain and Range from Graphs

识别域和函数范围的另一种方法是使用图形。由于属性域是指一组可能的输入值,因此图形的域由x-轴。范围是一组可能的输出值,这些值显示在和-轴。请记住,如果图形继续超出我们可以看到的图形部分,则域和范围可能大于可见值。请参阅图 8 。

我们可以观察到,该图从−5向右无界,因此域是[−5,∞).图形的垂直范围是所有范围值 5 及以下,因此范围为(−∞,5].请注意,域和范围始终从小值写入到较大值,或者从左到右写入域,范围始终从图形底部写入到图形顶部。

微积分网课代修|预备微积分代写precalculus辅导| Finding Domain and Range from a Graph

查找函数的域和范围f其图形如图 9 所示。

解决方案 我们可以观察到图形的水平范围是−3到 1,所以域f是(−3,1].
图形的垂直范围为 0 到−4,因此范围为[−4,0].请参阅图 10 。

解 沿水平轴的输入量是“年”,我们用变量表示t为了时间。输出量是“每天数千桶石油”,我们用变量表示b用于桶。图形可能会继续向左和向右移动,超出所查看的内容,但根据图形中可见的部分,我们可以将域确定为1973≤吨≤2008和范围约为2010≤180≤.

微积分网课代修|预备微积分代写precalculus辅导|MATH165 Finding Domain and Range from Graphs
微积分网课代修|预备微积分代写precalculus辅导

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