At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Certainly! Let's first graph the set \(\{x \mid -7 \leq x \leq 5\}\) on a number line, and then we'll express it using interval notation.
### Step-by-Step Solution:
1. Understanding the Set:
The given set is \(\{x \mid -7 \leq x \leq 5\}\), which means we are looking at all values of \(x\) between \(-7\) and \(5\), including the endpoints \(-7\) and \(5\).
2. Graphing on the Number Line:
To graph the set on the number line, we need to mark and shade the portion of the number line from \(-7\) to \(5\).
- Draw a horizontal line to represent the number line.
- Mark the points \(-7\) and \(5\) on this line.
- Shade the region between \(-7\) and \(5\) to indicate all the points \(x\) such that \(-7 \leq x \leq 5\).
- Use a solid dot or circle at \(-7\) and \(5\) to show that these endpoints are included in the set.
Here's how it would look like graphically:
```
-10 -8 -6 -4 -2 0 2 4 6 8 10
|------|------|------|------|------|------|------|------|------|------|
•------------------------------------•
-7 5
```
3. Interval Notation:
Interval notation is a concise way of writing the set of numbers between two endpoints.
Since \(-7\) and \(5\) are included in the set, we use square brackets \([ \ ]) to denote that the endpoints are included.
Therefore, the interval notation for the set \(\{x \mid -7 \leq x \leq 5\}\) is:
[tex]\[ [-7, 5] \][/tex]
### Summary
- Graph:
On a number line, shade the portion between \(-7\) and \(5\), including the endpoints.
- Interval Notation:
[tex]\[ [-7, 5] \][/tex]
This concludes the steps to graph the set and write it in interval notation.
### Step-by-Step Solution:
1. Understanding the Set:
The given set is \(\{x \mid -7 \leq x \leq 5\}\), which means we are looking at all values of \(x\) between \(-7\) and \(5\), including the endpoints \(-7\) and \(5\).
2. Graphing on the Number Line:
To graph the set on the number line, we need to mark and shade the portion of the number line from \(-7\) to \(5\).
- Draw a horizontal line to represent the number line.
- Mark the points \(-7\) and \(5\) on this line.
- Shade the region between \(-7\) and \(5\) to indicate all the points \(x\) such that \(-7 \leq x \leq 5\).
- Use a solid dot or circle at \(-7\) and \(5\) to show that these endpoints are included in the set.
Here's how it would look like graphically:
```
-10 -8 -6 -4 -2 0 2 4 6 8 10
|------|------|------|------|------|------|------|------|------|------|
•------------------------------------•
-7 5
```
3. Interval Notation:
Interval notation is a concise way of writing the set of numbers between two endpoints.
Since \(-7\) and \(5\) are included in the set, we use square brackets \([ \ ]) to denote that the endpoints are included.
Therefore, the interval notation for the set \(\{x \mid -7 \leq x \leq 5\}\) is:
[tex]\[ [-7, 5] \][/tex]
### Summary
- Graph:
On a number line, shade the portion between \(-7\) and \(5\), including the endpoints.
- Interval Notation:
[tex]\[ [-7, 5] \][/tex]
This concludes the steps to graph the set and write it in interval notation.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.