https://file.aiquickdraw.com/mathbot/file/1726532212723fryvo5ku.jpg

I see you've uploaded an image containing multiple-choice math questions. Let's go through each question to determine the correct answers.

### Questions and Answers:

1. **Which of the following is an exponential function?**
   - **Answer:** A. \( y = 5^x \)
   - Reason: It's the only function where the variable \( x \) is in the exponent, defining it as an exponential function.

2. **Which could be the set of ordered pairs of the function \( f(x) = 2^x + 3 \)?**
   - **Answer:** B.
   - Reason: Calculation for each \( x \) value in option B matches the function \( f(x) = 2^x + 3 \). For example, \( f(-2) = 2^{-2} + 3 = 0.25 + 3 = 3.25 \).

3. **Determine the set range of the function \( f(x) = 2^x + 3 \).**
   - **Answer:** C. \( (3, \infty) \)
   - Reason: Since \( 2^x \) ranges from \( 0 \) to \( \infty \) (excluding \( 0 \)), adding \( 3 \) shifts the entire range up by \( 3 \).

4. **Determine the set of domain of the function \( f(x) = 2^x + 3 \).**
   - **Answer:** A. set of real numbers
   - Reason: The domain of an exponential function is all real numbers.

5. **What is the horizontal asymptote of the function \( f(x) = 2^x + 3 \)?**
   - **Answer:** B. \( x = 3 \)
   - Reason: As \( x \) approaches negative infinity, \( 2^x \) approaches \( 0 \), so \( f(x) \) approaches \( 3 \), making \( y = 3 \) the horizontal asymptote.

6. **What is the zero of a function?**
   - **Answer:** B. \( x = 0 \)
   - Reason: The zero of a function is where the function crosses the x-axis, i.e., \( f(x) = 0 \).

7. **What happened to the values of y as x decreases?**
   - **Answer:** C. approaches to 0
   - Reason: The graph is an exponential decay graph, so as \( x \) decreases, \( y \) values approach \( 0 \).

8. **What are the intercepts of the function?**
   - **Answer:** B. \( x = 0 \), \( y = 0 \)
   - Reason: The graph crosses both axes at the origin (0,0).

9. **What are the sets of domain and range?**
   - **Answer:** C. \( D: (-\infty, \infty) \), \( R: (-3, \infty) \)
   - Reason: The domain of an exponential function is all real numbers, and the range is all real numbers above -3, given the graph's downward shift.

10. **What is the horizontal asymptote of the given graph of a function?**
    - **Answer:** A. \( y = -3 \)
    - Reason: The graph approaches \( y = -3 \) as \( x \) moves towards positive infinity.

Please review the answers, and let me know if you'd like more details on any specific question or topic!

#### Additional Questions:
1. Why does the range of an exponential function \( 2^x + 3 \) start from \( 3 \) and not \( 0 \)?
2. How would changing the base of the exponential affect the graph and its properties?
3. What would happen to the graph if we subtracted a number instead of adding 3?
4. Can you explain the concept of exponential growth and decay in more detail?
5. What are other types of asymptotes, and how are they determined from the equation of a function?

#### Tip:
Remember, for exponential functions like \( f(x) = a^x + k \), the graph's behavior (growth or decay) depends on whether \( a \) is greater than or less than 1, and the horizontal asymptote is determined by the constant \( k \).

Multiple-choice math questions focusing on exponential functions, intercepts, domain, range, and asymptotes.

Solve multiple-choice questions about exponential functions, intercepts, domain, range, and asymptotes. Includes detailed step-by-step solutions for each problem, suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation