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True or False. The function y = f(x) has the property that the slope always increases as increases. 5 Ay 4 3 2 1 O True O False -5 -4 -3 -2 -11 -2 -3 -4 -5 - y = f(x) 3 4 5 O

True or False. The function y = f(x) has the property that the slope always increases as increases. 5 Ay 4 3 2 1 O True O False -5 -4 -3 -2 -11 -2 -3 -4 -5 - y = f(x) 3 4 5 O

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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**True or False.** The function \( y = f(x) \) has the property that the slope always increases as \( x \) increases. **Graph Explanation:** The graph shows a downward-opening parabola, representing the function \( y = f(x) \). It is symmetric about the y-axis and reaches a maximum at the vertex, which is located at the point \( (0, 4) \). - The x-axis ranges from -5 to 5. - The y-axis ranges from -5 to 5. - The parabola passes through the points approximately \((-3, -5)\), \((-2, 0)\), \((0, 4)\), \((2, 0)\), and \((3, -5)\). **Interpretation:** - The slope of the function is positive as \( x \) increases from negative values to zero, reaches zero at the vertex, and then becomes negative as \( x \) continues to increase beyond zero. - Therefore, the slope does not always increase as \( x \) increases. **Answer Options:** - ○ True - ○ False
Transcribed Image Text:**True or False.** The function \( y = f(x) \) has the property that the slope always increases as \( x \) increases. **Graph Explanation:** The graph shows a downward-opening parabola, representing the function \( y = f(x) \). It is symmetric about the y-axis and reaches a maximum at the vertex, which is located at the point \( (0, 4) \). - The x-axis ranges from -5 to 5. - The y-axis ranges from -5 to 5. - The parabola passes through the points approximately \((-3, -5)\), \((-2, 0)\), \((0, 4)\), \((2, 0)\), and \((3, -5)\). **Interpretation:** - The slope of the function is positive as \( x \) increases from negative values to zero, reaches zero at the vertex, and then becomes negative as \( x \) continues to increase beyond zero. - Therefore, the slope does not always increase as \( x \) increases. **Answer Options:** - ○ True - ○ False
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