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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Question
![**Evaluating and Simplifying the Difference Quotient for Linear Functions**
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For the function \( f(x) = 5x - 4 \), evaluate and simplify the difference quotient:
\[ \frac{f(x+h) - f(x)}{h} \]
---
**Solution Approach:**
1. **Substitute \( f(x) \) and \( f(x+h) \) into the difference quotient:**
The function given is \( f(x) = 5x - 4 \).
Hence, \( f(x + h) = 5(x + h) - 4 \).
2. **Simplify \( f(x + h) \):**
\[ f(x + h) = 5(x + h) - 4 \]
\[ = 5x + 5h - 4 \]
3. **Calculate \( f(x + h) - f(x) \):**
\[ f(x + h) - f(x) = (5x + 5h - 4) - (5x - 4) \]
\[ = 5x + 5h - 4 - 5x + 4 \]
\[ = 5h \]
4. **Divide by \( h \):**
\[ \frac{f(x + h) - f(x)}{h} = \frac{5h}{h} = 5 \]
**Final simplified form:**
\[ \frac{f(x + h) - f(x)}{h} = 5 \]
---
For further assistance, please refer to the video tutorial linked below:
[**Question Help: Video**]
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End of transcription.
(Note: There is an icon indicating a video is available if extra help is needed. The bottom of the image displays system icons and notifications along with weather information. These elements are likely not relevant to the educational content but indicate it was captured from a digital device.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76c19111-0832-474a-9997-f0da2ac47ca4%2F8436b780-a3eb-410c-bffa-25d9169a480e%2F5da2s8q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluating and Simplifying the Difference Quotient for Linear Functions**
---
For the function \( f(x) = 5x - 4 \), evaluate and simplify the difference quotient:
\[ \frac{f(x+h) - f(x)}{h} \]
---
**Solution Approach:**
1. **Substitute \( f(x) \) and \( f(x+h) \) into the difference quotient:**
The function given is \( f(x) = 5x - 4 \).
Hence, \( f(x + h) = 5(x + h) - 4 \).
2. **Simplify \( f(x + h) \):**
\[ f(x + h) = 5(x + h) - 4 \]
\[ = 5x + 5h - 4 \]
3. **Calculate \( f(x + h) - f(x) \):**
\[ f(x + h) - f(x) = (5x + 5h - 4) - (5x - 4) \]
\[ = 5x + 5h - 4 - 5x + 4 \]
\[ = 5h \]
4. **Divide by \( h \):**
\[ \frac{f(x + h) - f(x)}{h} = \frac{5h}{h} = 5 \]
**Final simplified form:**
\[ \frac{f(x + h) - f(x)}{h} = 5 \]
---
For further assistance, please refer to the video tutorial linked below:
[**Question Help: Video**]
---
End of transcription.
(Note: There is an icon indicating a video is available if extra help is needed. The bottom of the image displays system icons and notifications along with weather information. These elements are likely not relevant to the educational content but indicate it was captured from a digital device.)
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