# 微积分网课代修|预备微积分代写precalculus辅导|MATH1730 Using Notations to Specify Domain and Range

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分网课代修|预备微积分代写precalculus辅导|Using Notations to Specify Domain and Range

In the previous examples, we used inequalities and lists to describe the domain of functions. We can also use inequalities, or other statements that might define sets of values or data, to describe the behavior of the variable in set-builder notation. For example, ${x \mid 10 \leq x<30}$ describes the behavior of $x$ in set-builder notation. The braces {} are read as “the set of,” and the vertical bar $\mid$ is read as “such that,” so we would read ${x \mid 10 \leq x<30}$ as “the set of $x$-values such that 10 is less than or equal to $x$, and $x$ is less than $30 . “$
Figure 5 compares inequality notation, set-builder notation, and interval notation.

To combine two intervals using inequality notation or set-builder notation, we use the word “or.” As we saw in earlier examples, we use the union symbol, $\cup$, to combine two unconnected intervals. For example, the union of the sets ${2,3,5}$ and ${4,6}$ is the set ${2,3,4,5,6}$. It is the set of all elements that belong to one or the other (or both) of the original two sets. For sets with a finite number of elements like these, the elements do not have to be listed in ascending order of numerical value. If the original two sets have some elements in common, those elements should be listed only once in the union set. For sets of real numbers on intervals, another example of a union is
$${x|| x \mid \geq 3}=(-\infty,-3] \cup[3, \infty)$$

## 微积分网课代修|预备微积分代写precalculus辅导|set-builder notation and interval notation

Set-builder notation is a method of specifying a set of elements that satisfy a certain condition. It takes the form ${x \mid$ statement about $x}$ which is read as, “the set of all $x$ such that the statement about $x$ is true.” For example,
$${x \mid 4<x \leq 12}$$
Interval notation is a way of describing sets that include all real numbers between a lower limit that may or may not be included and an upper limit that may or may not be included. The endpoint values are listed between brackets or parentheses. A square bracket indicates inclusion in the set, and a parenthesis indicates exclusion from the set. For example,
$(4,12]$

## 微积分网课代修预备微积分代写precalculus辅导| Using Notations to Specify Domain and Range

$$x|| x \mid \geq 3=(-\infty,-3] \cup[3, \infty)$$