Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Transcription and Analysis for Educational Website**

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**Task:**

Find the exponential function that represents the graph shown.

**Graph Description:**

The graph presented is a downward-sloping exponential curve, starting from high positive values on the left and approaching zero as it moves to the right. The x-axis ranges from -5 to 5, and the y-axis ranges from -2 to 18. The red curve demonstrates exponential decay.

**Multiple-Choice Options:**

1. \( f(x) = \frac{1}{2} \cdot 4^x \)

2. \( f(x) = 4 \left( \frac{1}{4} \right)^x \)

3. \( f(x) = 2^x \)

4. \( f(x) = 4 \left( \frac{1}{2} \right)^x \)

**Explanation of the Graph:**

- The graph shows exponential decay, typically characterized by a function where the base of the exponent is between 0 and 1.
- The behavior of the graph suggests it matches one of the given functions based on its asymptotic trend towards the x-axis.

**Conclusion:**

Analyze the functions to determine which one represents the graph accurately. Functions with a base of less than 1 in the exponent will show decay, similar to the red curve in the graph.
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Transcribed Image Text:**Transcription and Analysis for Educational Website** --- **Task:** Find the exponential function that represents the graph shown. **Graph Description:** The graph presented is a downward-sloping exponential curve, starting from high positive values on the left and approaching zero as it moves to the right. The x-axis ranges from -5 to 5, and the y-axis ranges from -2 to 18. The red curve demonstrates exponential decay. **Multiple-Choice Options:** 1. \( f(x) = \frac{1}{2} \cdot 4^x \) 2. \( f(x) = 4 \left( \frac{1}{4} \right)^x \) 3. \( f(x) = 2^x \) 4. \( f(x) = 4 \left( \frac{1}{2} \right)^x \) **Explanation of the Graph:** - The graph shows exponential decay, typically characterized by a function where the base of the exponent is between 0 and 1. - The behavior of the graph suggests it matches one of the given functions based on its asymptotic trend towards the x-axis. **Conclusion:** Analyze the functions to determine which one represents the graph accurately. Functions with a base of less than 1 in the exponent will show decay, similar to the red curve in the graph.
Expert Solution
Check Mark
Step 1

Topic = Function

Correct option    f(x)=412x 

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