A graph of the exponential function g(x) is given. 24 22 g(x) 20 18 16 14 12 10 B 6 4 2 -3 -2 -1 0 O g(x) = 5x Write the equation to represent g(x). g(x) = 5₁ (²) * Og(x) = 5.5x ○ g(x) = ( 1² ) * 3

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Exponential Function Graph and Equation

The graph displayed is of an exponential function \( g(x) \).

#### Graph Details:
- The vertical axis (\( y \)) marks values from 0 to 24.
- The horizontal axis (\( x \)) ranges from -3 to 3.
- The curve starts from a high value on the left and decreases rapidly, flattening as it moves to the right, indicating a decay function.
- Specific points include \( g(-3) = 24 \), \( g(-2) = 12\), \( g(-1) = 6\), \( g(0) = 5 \), \( g(1) = 1 \), \( g(2) = 0.2 \).

#### Task:
Write the equation to represent \( g(x) \).

#### Options:
1. \( g(x) = 5 \cdot \left( \frac{1}{5} \right)^x \)
2. \( g(x) = 5 \cdot 5^x \)
3. \( g(x) = \left( \frac{1}{5} \right)^x \)
4. \( g(x) = 5^x \)

The correct representation for \( g(x) \) can be determined by the pattern of values and the decay behavior observed in the graph.
Transcribed Image Text:### Exponential Function Graph and Equation The graph displayed is of an exponential function \( g(x) \). #### Graph Details: - The vertical axis (\( y \)) marks values from 0 to 24. - The horizontal axis (\( x \)) ranges from -3 to 3. - The curve starts from a high value on the left and decreases rapidly, flattening as it moves to the right, indicating a decay function. - Specific points include \( g(-3) = 24 \), \( g(-2) = 12\), \( g(-1) = 6\), \( g(0) = 5 \), \( g(1) = 1 \), \( g(2) = 0.2 \). #### Task: Write the equation to represent \( g(x) \). #### Options: 1. \( g(x) = 5 \cdot \left( \frac{1}{5} \right)^x \) 2. \( g(x) = 5 \cdot 5^x \) 3. \( g(x) = \left( \frac{1}{5} \right)^x \) 4. \( g(x) = 5^x \) The correct representation for \( g(x) \) can be determined by the pattern of values and the decay behavior observed in the graph.
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