Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.1: Relations And Functions
Problem 75PS
Related questions
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:
\[ \frac{f(x+h) - f(x)}{h} \]
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**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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