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Expert-verified Found in: Page 11 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Graph the set$\left[-4,6\right)\cup \left[0,8\right)$

The graph of the given set is, See the step by step solution

## Step 1. Apply the concept of interval and number line.

If $a, then the open interval from a to b consists of all numbers between a and b and is denoted by $\left(a,b\right)$. The closed interval from a to b includes the endpoints and is denoted by $\left[a,b\right]$. If points are included in the interval, they are represented by dark circles and if the points are not included in the interval, they are represented by hollow circles on the number line.

Using the set-builder form, we can write the intervals as inequality: $\left(a,b\right)=\left\{x|a

## Step 2. Apply the concept of the union of sets.

If S and T are set, then their union $S\cup T$ is the set that consists of all elements that are in S or T (or in both).

## Step 3. Find the union.

$\begin{array}{l}\left[-4,6\right)\cup \left[0,8\right)\\ =\left\{x|-4\le x<6\right\}\cup \left\{x|0\le x<8\right\}\\ =\left\{x|-4\le x<6\text{or}0\le x<8\right\}\\ =\left\{x|-4\le x<8\right\}\\ =\left[-4,8\right)\end{array}$

## Step 4. Graph the intervals.

We will graph all three intervals:

$\left[-4,6\right)$

It includes all the numbers between -4 and 6, including -4. $\left[0,8\right)$

It includes all the numbers between 0 and 8, including 0. $\left[-4,6\right)\cup \left[0,8\right)=\left[-4,8\right)$

It includes all the numbers between -4 and 8, including -4.  ### Want to see more solutions like these? 