Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Function Analysis Worksheet**
**Function:**
\[ f(x) = \frac{2x - 3}{2x - 8} \]
**Analysis Requirements:**
1. **Domain:**
- Describe the set of all possible input values (x) for f(x).
2. **Vertical Asymptotes (V.A.):**
- Identify the value of x where the function approaches infinity.
3. **Horizontal Asymptotes (H.A.):**
- Determine the y-value that the function approaches as x tends to infinity.
4. **Critical Points (Crit. Pts.):**
- Find the x-values where the first derivative of the function is zero or undefined.
5. **Intervals of Increase (Incr.):**
- Identify the intervals where the function is increasing.
6. **Intervals of Decrease (Decr.):**
- Identify the intervals where the function is decreasing.
7. **Concavity (Conc.):**
- **Conc. Up:** Specify the intervals where the function is concave up.
- **Conc. Down:** Specify the intervals where the function is concave down.
8. **Inflection Points (Infl. Pts.):**
- Determine the x-values where the concavity changes.
**Graph Explanation:**
- The graph features a typical Cartesian plane with the x-axis and y-axis clearly marked.
- Both axes show tick marks at integer values, ranging from -4 to 4.
- The grid lines provide guidance for plotting points and interpreting the layout of the function graphically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2cc25c0-e9ff-48be-a0df-5f141951a1aa%2Ff541e69d-6239-42e1-baaa-031df43464bf%2Flnylfuc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Function Analysis Worksheet**
**Function:**
\[ f(x) = \frac{2x - 3}{2x - 8} \]
**Analysis Requirements:**
1. **Domain:**
- Describe the set of all possible input values (x) for f(x).
2. **Vertical Asymptotes (V.A.):**
- Identify the value of x where the function approaches infinity.
3. **Horizontal Asymptotes (H.A.):**
- Determine the y-value that the function approaches as x tends to infinity.
4. **Critical Points (Crit. Pts.):**
- Find the x-values where the first derivative of the function is zero or undefined.
5. **Intervals of Increase (Incr.):**
- Identify the intervals where the function is increasing.
6. **Intervals of Decrease (Decr.):**
- Identify the intervals where the function is decreasing.
7. **Concavity (Conc.):**
- **Conc. Up:** Specify the intervals where the function is concave up.
- **Conc. Down:** Specify the intervals where the function is concave down.
8. **Inflection Points (Infl. Pts.):**
- Determine the x-values where the concavity changes.
**Graph Explanation:**
- The graph features a typical Cartesian plane with the x-axis and y-axis clearly marked.
- Both axes show tick marks at integer values, ranging from -4 to 4.
- The grid lines provide guidance for plotting points and interpreting the layout of the function graphically.
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