Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Finding the x-intercepts (horizontal intercepts) of the Function**
To find the x-intercepts (horizontal intercepts) of the function \(f(x) = 4|x + 1| - 2\), follow these steps:
The x-intercepts are the values of \(x\) where the function \(f(x)\) is equal to zero. This means you need to solve the equation:
\[ 0 = 4|x + 1| - 2 \]
To solve for \(x\):
1. **Isolate the absolute value expression:**
\[ 4|x + 1| = 2 \]
2. **Divide both sides by 4:**
\[ |x + 1| = \frac{2}{4} \]
\[ |x + 1| = \frac{1}{2} \]
3. **Set up two equations to remove the absolute value:**
\( x + 1 = \frac{1}{2} \)
\( x + 1 = -\frac{1}{2} \)
4. **Solve each equation for \(x\):**
For \( x + 1 = \frac{1}{2} \):
\[ x = \frac{1}{2} - 1 \]
\[ x = \frac{1}{2} - \frac{2}{2} \]
\[ x = -\frac{1}{2} \]
For \( x + 1 = -\frac{1}{2} \):
\[ x = -\frac{1}{2} - 1 \]
\[ x = -\frac{1}{2} - \frac{2}{2} \]
\[ x = -\frac{3}{2} \]
Therefore, the intercepts are at \( x = -\frac{1}{2}, -\frac{3}{2} \).
**Separating Values with Commas**
Make sure to separate the x-intercepts with commas when listing them. For example:
\[ x = -\frac{1}{2}, -\frac{3}{2} \]
**Question Help:**
If you need further assistance in understanding how to find x-intercepts, you may watch this helpful video by clicking on the video link provided.
**End](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6691cd2-55cd-462f-8290-5296a9107f11%2F7dba2195-7018-4a4f-bc5f-1fb6eb93433c%2Fdn6kr99_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the x-intercepts (horizontal intercepts) of the Function**
To find the x-intercepts (horizontal intercepts) of the function \(f(x) = 4|x + 1| - 2\), follow these steps:
The x-intercepts are the values of \(x\) where the function \(f(x)\) is equal to zero. This means you need to solve the equation:
\[ 0 = 4|x + 1| - 2 \]
To solve for \(x\):
1. **Isolate the absolute value expression:**
\[ 4|x + 1| = 2 \]
2. **Divide both sides by 4:**
\[ |x + 1| = \frac{2}{4} \]
\[ |x + 1| = \frac{1}{2} \]
3. **Set up two equations to remove the absolute value:**
\( x + 1 = \frac{1}{2} \)
\( x + 1 = -\frac{1}{2} \)
4. **Solve each equation for \(x\):**
For \( x + 1 = \frac{1}{2} \):
\[ x = \frac{1}{2} - 1 \]
\[ x = \frac{1}{2} - \frac{2}{2} \]
\[ x = -\frac{1}{2} \]
For \( x + 1 = -\frac{1}{2} \):
\[ x = -\frac{1}{2} - 1 \]
\[ x = -\frac{1}{2} - \frac{2}{2} \]
\[ x = -\frac{3}{2} \]
Therefore, the intercepts are at \( x = -\frac{1}{2}, -\frac{3}{2} \).
**Separating Values with Commas**
Make sure to separate the x-intercepts with commas when listing them. For example:
\[ x = -\frac{1}{2}, -\frac{3}{2} \]
**Question Help:**
If you need further assistance in understanding how to find x-intercepts, you may watch this helpful video by clicking on the video link provided.
**End
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