Chapter 1.5, Problem 12E

To determine

To express: the given graph in interval notation.

Answer to Problem 12E

In terms of interval the set can be expressed as $\left(-\infty ,-1.5\right]\cup \left[1.5,\infty \right)$ .

Explanation of Solution

Given information:

A graph is given as

Concept used:

An inequality $a<x<b$ in terms of an interval can be expressed as $\left(a,b\right)$ .

An inequality $a\le x\le b$ in terms of an interval can be expressed as $\left[a,b\right]$ .

An inequality $a\le x<b$ in terms of an interval can be expressed as $\left[a,b\right)$ .

An inequality $a<x\le b$ in terms of an interval can be expressed as $\left(a,b\right]$ .

An inequality $x\le b$ in terms of an interval can be expressed as $\left(-\infty ,b\right]$ .

An inequality $x<b$ in terms of an interval can be expressed as $\left(-\infty ,b\right)$ .

An inequality $x\ge a$ in terms of an interval can be expressed as $\left[a,\infty \right)$ .

An inequality $x>a$ in terms of an interval can be expressed as $\left(a,\infty \right)$ .

If the terminal number or point is included in the interval it can be represented by closed ball on the number line otherwise it will be represented by an open ball.

Calculation:

Consider the given graph.

Here, for both $-1.5$ and $1.5$ closed balls are placed on the number line, so both will be included to the interval.

So, the set can be expressed as an interval as $\left(-\infty ,-1.5\right]\cup \left[1.5,\infty \right)$ .