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Graph the function by applying an appropriate reflection. k (x)=(-x)³ 6+ 4- 2- -8 -6 -4 -2 6. 4 -2- -4- 6+ 2. 8. to

Graph the function by applying an appropriate reflection. k (x)=(-x)³ 6+ 4- 2- -8 -6 -4 -2 6. 4 -2- -4- 6+ 2. 8. to

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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**Title: Graphing Reflected Functions** **Objective:** Learn how to graph functions after applying reflections. **Function:** The given function is \( k(x) = (-x)^3 \). **Task:** Graph the function by applying an appropriate reflection. **Graph Description:** The graph is represented on a coordinate plane with both x and y axes ranging from -8 to 8. The plotted function, \( k(x) = (-x)^3 \), appears as a blue curve. **Function Analysis:** 1. **Symmetry and Reflection:** - The function \( k(x) = (-x)^3 \) can be considered a reflection of \( x^3 \) across the y-axis. - This reflects all points such that if a point (x, y) is on the original \( x^3 \) graph, then the point (-x, y) is on the reflected graph. 2. **Shape of the Graph:** - The graph shows typical cubic behavior: it passes through the origin (0,0). - As x approaches 8, y increases rapidly, and as x approaches -8, y decreases. 3. **Transformations:** - Since the graph is \( (-x)^3 \), this is reflected over the y-axis compared to the graph of \( x^3 \). **Interactive Features:** - **Transform Tools:** - The interface includes options for manipulating the graph: - An arrow cross indicates the capability to move the graph. - A trapezoid shape suggests a zoom feature to expand or contract the view. - A reset symbol is available for undoing changes and resetting the graph. **Conclusion:** Understanding reflections allows for better mastery of function transformations and their graphical representations. Use the interactive features to practice applying reflections and observe their effects on various functions. **Action Button:** "Check" - Click to verify your graph against the correct reflective transformation.
Transcribed Image Text:**Title: Graphing Reflected Functions** **Objective:** Learn how to graph functions after applying reflections. **Function:** The given function is \( k(x) = (-x)^3 \). **Task:** Graph the function by applying an appropriate reflection. **Graph Description:** The graph is represented on a coordinate plane with both x and y axes ranging from -8 to 8. The plotted function, \( k(x) = (-x)^3 \), appears as a blue curve. **Function Analysis:** 1. **Symmetry and Reflection:** - The function \( k(x) = (-x)^3 \) can be considered a reflection of \( x^3 \) across the y-axis. - This reflects all points such that if a point (x, y) is on the original \( x^3 \) graph, then the point (-x, y) is on the reflected graph. 2. **Shape of the Graph:** - The graph shows typical cubic behavior: it passes through the origin (0,0). - As x approaches 8, y increases rapidly, and as x approaches -8, y decreases. 3. **Transformations:** - Since the graph is \( (-x)^3 \), this is reflected over the y-axis compared to the graph of \( x^3 \). **Interactive Features:** - **Transform Tools:** - The interface includes options for manipulating the graph: - An arrow cross indicates the capability to move the graph. - A trapezoid shape suggests a zoom feature to expand or contract the view. - A reset symbol is available for undoing changes and resetting the graph. **Conclusion:** Understanding reflections allows for better mastery of function transformations and their graphical representations. Use the interactive features to practice applying reflections and observe their effects on various functions. **Action Button:** "Check" - Click to verify your graph against the correct reflective transformation.
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