Use the graph of f to sketch the graph of f. Then use the graphs to determine the domain and ange of each function. Ay 7 Q G OA. The domain off is. (Type your answer in interval notation.) The range of fis O B. G O D. The function does not ha
Use the graph of f to sketch the graph of f. Then use the graphs to determine the domain and ange of each function. Ay 7 Q G OA. The domain off is. (Type your answer in interval notation.) The range of fis O B. G O D. The function does not ha
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.4: Operations On Functions
Problem 123E
Related questions
Question
- The main graph shows a function \( f \) with a typical S-shape, crossing the origin, and increasing as \( x \) and \( y \) move away from zero.
- The dotted line represents the line \( y=x \), which acts as a reference for reflecting the function to find its inverse.
**Options for Inverse Graph:**
- **Option A:** A mirrored S-shape graph.
- **Option B:** An upright S-shape graph.
- **Option C:** A graph similar to Option A but horizontally flipped.
- **Option D:** Indicates that the function does not have an inverse.
3. **Domain and Range Determination**
- Identify the domain and range of the function \( f \).
- **Domain:** The set of all possible input values \( x \).
- **Range:** The set of all possible output values \( y \).
**Fill in the Blanks:**
- **The domain of \( f \) is \( \_\_\_\_ \).**
- (Type your answer in interval notation.)
- **The range of \( f \) is \( \_\_\_\_ \).**
- (Type your answer in interval notation.)
**Example Answer:**
- **The domain of \( f \) is \( (-\infty, \infty) \).**
- **The range of \( f \) is \( (-\infty, \infty) \).**
Choose the correct graph of the inverse below:
- [ ] A.
- [ ] B.
- [ ] C.
- [ ] D. The function does not have an inverse](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c3541e1-5e06-431d-ac0c-cc0370504735%2Fbff14f88-0aed-4859-9d4b-5325913eddcb%2Fd1u2js4_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Inverses and Determining Domain and Range
#### Exercise: Sketching the Inverse Graph and Identifying Domain & Range
**Instructions:**
1. **Graph Analysis**
- Use the graph of the function \( f \) given on the left side of the screen to sketch the graph of \( f^{-1} \).
2. **Graph Identification**
- Choose the correct graph of the inverse from the provided options.
- The main graph shows a function \( f \) with a typical S-shape, crossing the origin, and increasing as \( x \) and \( y \) move away from zero.
- The dotted line represents the line \( y=x \), which acts as a reference for reflecting the function to find its inverse.
**Options for Inverse Graph:**
- **Option A:** A mirrored S-shape graph.
- **Option B:** An upright S-shape graph.
- **Option C:** A graph similar to Option A but horizontally flipped.
- **Option D:** Indicates that the function does not have an inverse.
3. **Domain and Range Determination**
- Identify the domain and range of the function \( f \).
- **Domain:** The set of all possible input values \( x \).
- **Range:** The set of all possible output values \( y \).
**Fill in the Blanks:**
- **The domain of \( f \) is \( \_\_\_\_ \).**
- (Type your answer in interval notation.)
- **The range of \( f \) is \( \_\_\_\_ \).**
- (Type your answer in interval notation.)
**Example Answer:**
- **The domain of \( f \) is \( (-\infty, \infty) \).**
- **The range of \( f \) is \( (-\infty, \infty) \).**
Choose the correct graph of the inverse below:
- [ ] A.
- [ ] B.
- [ ] C.
- [ ] D. The function does not have an inverse
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