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### Transformation of the Exponential Function The graph below illustrates a transformation of the exponential function \( y = 2^x \). **Graph Description:** - The graph is plotted on a Cartesian coordinate system with both axes ranging from -5 to 5. - The transformation displayed is a reflection of the exponential curve across the y-axis. This is indicated by the graph approaching the x-axis from the left and decreasing as it moves to the right. **Task:** - You are asked to write an equation for the transformed graph. **Explanation:** This transformation involves reflecting the original exponential function across the y-axis, which suggests the equation of the graph is \( y = 2^{-x} \). This transformation maintains the general nature of the curve but changes its orientation.

### Transformation of the Exponential Function The graph below illustrates a transformation of the exponential function \( y = 2^x \). **Graph Description:** - The graph is plotted on a Cartesian coordinate system with both axes ranging from -5 to 5. - The transformation displayed is a reflection of the exponential curve across the y-axis. This is indicated by the graph approaching the x-axis from the left and decreasing as it moves to the right. **Task:** - You are asked to write an equation for the transformed graph. **Explanation:** This transformation involves reflecting the original exponential function across the y-axis, which suggests the equation of the graph is \( y = 2^{-x} \). This transformation maintains the general nature of the curve but changes its orientation.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Transformation of the Exponential Function The graph below illustrates a transformation of the exponential function \( y = 2^x \). **Graph Description:** - The graph is plotted on a Cartesian coordinate system with both axes ranging from -5 to 5. - The transformation displayed is a reflection of the exponential curve across the y-axis. This is indicated by the graph approaching the x-axis from the left and decreasing as it moves to the right. **Task:** - You are asked to write an equation for the transformed graph. **Explanation:** This transformation involves reflecting the original exponential function across the y-axis, which suggests the equation of the graph is \( y = 2^{-x} \). This transformation maintains the general nature of the curve but changes its orientation.
Transcribed Image Text:### Transformation of the Exponential Function The graph below illustrates a transformation of the exponential function \( y = 2^x \). **Graph Description:** - The graph is plotted on a Cartesian coordinate system with both axes ranging from -5 to 5. - The transformation displayed is a reflection of the exponential curve across the y-axis. This is indicated by the graph approaching the x-axis from the left and decreasing as it moves to the right. **Task:** - You are asked to write an equation for the transformed graph. **Explanation:** This transformation involves reflecting the original exponential function across the y-axis, which suggests the equation of the graph is \( y = 2^{-x} \). This transformation maintains the general nature of the curve but changes its orientation.
Expert Solution
Step 1

The given graph is a transformation of y=2x.

The general equation is given as y=a2x+d.

From the graph Asymptote is y=3.

Therefore the equation is y=a2x+3

The points from the graph are:

A=1,-1 and B=(2,-5).

Substitute 1 for x and -1 for y in the equation y=a2x+3 to determine a.

-1=a(2)1+32a=-1-3a=-42a=-2

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