https://file.aiquickdraw.com/mathbot/file/17283204612773tbaud3a.jpg

To determine which graph corresponds to which function, let's analyze the two functions and the graphs:

1. **Function #1: \( f(x) = \left(\frac{1}{3}\right)^x \)**  
   This is an exponential decay function because the base, \( \frac{1}{3} \), is less than 1. As \( x \) increases, the function value decreases. As \( x \) decreases, the function value increases. So, the graph should show a decreasing behavior as we move right along the \( x \)-axis and increasing as we move left.

2. **Function #2: \( f(x) = 3^x \)**  
   This is an exponential growth function because the base, 3, is greater than 1. As \( x \) increases, the function value grows rapidly, and as \( x \) decreases, the function value approaches 0.

### Graph Analysis:

- **Graph i** shows exponential growth: As \( x \) increases, \( y \) increases rapidly, suggesting this graph corresponds to an exponential growth function. Hence, **Graph i** represents **Function #2: \( f(x) = 3^x \)**.
  
- **Graph ii** shows exponential decay: As \( x \) increases, \( y \) decreases, which is consistent with the behavior of an exponential decay function. Therefore, **Graph ii** corresponds to **Function #1: \( f(x) = \left(\frac{1}{3}\right)^x \)**.

### Conclusion:
- **Graph i** matches **Function #2: \( f(x) = 3^x \)**
- **Graph ii** matches **Function #1: \( f(x) = \left(\frac{1}{3}\right)^x \)**

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the general form of an exponential function?
2. How does changing the base of an exponential function affect its graph?
3. What happens to exponential growth functions as \( x \) approaches infinity?
4. How can we distinguish between exponential growth and decay by looking at their graphs?
5. What are the real-world applications of exponential growth and decay?

**Tip:** Exponential functions with bases greater than 1 show growth, while those with bases between 0 and 1 show decay.

Which graph belongs with which function? Graph i and Graph ii, where Function #1 is f(x) = (1/3)^x and Function #2 is f(x) = 3^x.

Learn how to distinguish between the graphs of exponential growth and decay functions. This problem matches f(x) = (1/3)^x to Graph ii (decay) and f(x) = 3^x to Graph i (growth). Suitable for high school math students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation