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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Identify the exponential function whose graph is given below
f(x)=
The graph presented is of an exponential function plotted on a Cartesian coordinate system. The horizontal axis (x-axis) ranges from -2 to 3, and the vertical axis (y-axis) ranges from -21 to 0. The graph demonstrates a downward curve, starting from just above the x-axis at x = -2, crossing the origin, and decreasing steeply as it moves to the right.
Key points of the graph:
- The function crosses the y-axis at (0,0).
- As x increases, the function decreases rapidly.
This graph represents a decreasing exponential function, suggesting that the function has the form \( f(x) = Ce^{kx} \) where C and k are constants, and k is negative.
Provide your answer below:
\[ f(x) = \] ______________
---
To correctly identify the exponential function, students need to:
1. Recognize the form of the exponential function.
2. Determine the constants from the shape and key points of the graph.
This problem helps reinforce the concept of exponential functions and their graphical representations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a313e2a-25da-4b9a-9850-84d0280d86f1%2Fc7adb764-0be7-47e8-afef-541f8f18453c%2Fu9pfqhl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question
Identify the exponential function whose graph is given below.
The graph presented is of an exponential function plotted on a Cartesian coordinate system. The horizontal axis (x-axis) ranges from -2 to 3, and the vertical axis (y-axis) ranges from -21 to 0. The graph demonstrates a downward curve, starting from just above the x-axis at x = -2, crossing the origin, and decreasing steeply as it moves to the right.
Key points of the graph:
- The function crosses the y-axis at (0,0).
- As x increases, the function decreases rapidly.
This graph represents a decreasing exponential function, suggesting that the function has the form \( f(x) = Ce^{kx} \) where C and k are constants, and k is negative.
Provide your answer below:
\[ f(x) = \] ______________
---
To correctly identify the exponential function, students need to:
1. Recognize the form of the exponential function.
2. Determine the constants from the shape and key points of the graph.
This problem helps reinforce the concept of exponential functions and their graphical representations.
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