Click here to view the transcript Consider the graph of the exponential function f(x) = 3². Which of the following statements are correct? (Select all that apply.) The graph crosses the x-axis. The graph has a horizontal asymptote at y = 0. The graph crosses the y-axis. The graph has a vertical asymptote at x = 0. As x increases, y also increases. As x increases, y decreases.
Click here to view the transcript Consider the graph of the exponential function f(x) = 3². Which of the following statements are correct? (Select all that apply.) The graph crosses the x-axis. The graph has a horizontal asymptote at y = 0. The graph crosses the y-axis. The graph has a vertical asymptote at x = 0. As x increases, y also increases. As x increases, y decreases.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![Certainly! Below is the transcribed text and a detailed description of any elements present:
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**Consider the graph of the exponential function \( f(x) = 3^x \). Which of the following statements are correct? (Select all that apply.)**
- [ ] The graph crosses the x-axis.
- [x] The graph has a horizontal asymptote at \( y = 0 \).
- [ ] The graph crosses the y-axis.
- [ ] The graph has a vertical asymptote at \( x = 0 \).
- [ ] As \( x \) increases, \( y \) also increases.
- [ ] As \( x \) increases, \( y \) decreases.
---
Explanation:
1. **Option 1: The graph crosses the x-axis.**
- This statement is incorrect. The graph of \( f(x) = 3^x \) never touches or crosses the x-axis as exponential functions of this form have a horizontal asymptote at \( y = 0 \).
2. **Option 2: The graph has a horizontal asymptote at \( y = 0 \).**
- This statement is correct. For the exponential function \( f(x) = 3^x \), as \( x \) tends to negative infinity, the value of \( f(x) \) approaches 0 but never actually reaches it. Hence, there is a horizontal asymptote at \( y = 0 \).
3. **Option 3: The graph crosses the y-axis.**
- This statement is incorrect. The exponential function \( f(x) = 3^x \) will intersect the y-axis at the point where \( x = 0 \). However, in typical graph-related terminology, 'crosses' usually implies that it intersects and continues beyond, which is not the case here.
4. **Option 4: The graph has a vertical asymptote at \( x = 0 \).**
- This statement is incorrect. There is no vertical asymptote for the function \( f(x) = 3^x \). As \( x \) increases or decreases, the function is defined for all real values of \( x \).
5. **Option 5: As \( x \) increases, \( y \) also increases.**
- This statement is correct. Since \( f(x) = 3^x \) is an exponential function](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb60d944d-b704-4774-a873-3518f4e82d9b%2Fb2f09add-24b1-40fd-aecb-84e488ef73a2%2Fisvhoan_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is the transcribed text and a detailed description of any elements present:
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**Consider the graph of the exponential function \( f(x) = 3^x \). Which of the following statements are correct? (Select all that apply.)**
- [ ] The graph crosses the x-axis.
- [x] The graph has a horizontal asymptote at \( y = 0 \).
- [ ] The graph crosses the y-axis.
- [ ] The graph has a vertical asymptote at \( x = 0 \).
- [ ] As \( x \) increases, \( y \) also increases.
- [ ] As \( x \) increases, \( y \) decreases.
---
Explanation:
1. **Option 1: The graph crosses the x-axis.**
- This statement is incorrect. The graph of \( f(x) = 3^x \) never touches or crosses the x-axis as exponential functions of this form have a horizontal asymptote at \( y = 0 \).
2. **Option 2: The graph has a horizontal asymptote at \( y = 0 \).**
- This statement is correct. For the exponential function \( f(x) = 3^x \), as \( x \) tends to negative infinity, the value of \( f(x) \) approaches 0 but never actually reaches it. Hence, there is a horizontal asymptote at \( y = 0 \).
3. **Option 3: The graph crosses the y-axis.**
- This statement is incorrect. The exponential function \( f(x) = 3^x \) will intersect the y-axis at the point where \( x = 0 \). However, in typical graph-related terminology, 'crosses' usually implies that it intersects and continues beyond, which is not the case here.
4. **Option 4: The graph has a vertical asymptote at \( x = 0 \).**
- This statement is incorrect. There is no vertical asymptote for the function \( f(x) = 3^x \). As \( x \) increases or decreases, the function is defined for all real values of \( x \).
5. **Option 5: As \( x \) increases, \( y \) also increases.**
- This statement is correct. Since \( f(x) = 3^x \) is an exponential function
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