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) through (c) to the right. Ay f(x) 2 20 Jh To -2- OA. -2≤x≤4 OB. x=0 O C. -2≤x<0, 0

) through (c) to the right. Ay f(x) 2 20 Jh To -2- OA. -2≤x≤4 OB. x=0 O C. -2≤x<0, 0

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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**Graph Analysis and Questions on Differentiability and Continuity** The figure on the left shows the graph of a function \( y = f(x) \) over the closed interval \(-2 \leq x \leq 4\). The function is depicted with blue lines and solid dots to indicate closed intervals and open dots for open intervals. **Graph Description:** - The graph consists of two segments. - The first segment ranges from \((-2, 0)\) to \((0, 2)\). - The second segment is a curve starting just after \((0, 2)\) and extends to \((4, -3)\). **Key Points:** - The function appears to be continuous and differentiable from \(-2 \leq x < 0\) and \(0 < x \leq 4\). - At \(x = 0\), the function appears to be neither continuous nor differentiable due to a break in the graph. **Questions:** a. **At what domain points does the function appear to be differentiable?** - A. \(-2 \leq x \leq 4\) - B. \(x = 0\) - C. \(-2 \leq x < 0, 0 < x \leq 4\) - D. None **Correct Answer: C** b. **At what domain points does the function appear to be continuous but not differentiable?** - A. \(-2 \leq x \leq 4\) - B. \(-2 \leq x < 0, 0 < x \leq 4\) - C. \(x = 0\) - D. None **Correct Answer: D** c. **At what domain points does the function appear to be neither continuous nor differentiable?** - A. \(-2 \leq x \leq 4\) - B. \(-2 \leq x < 0, 0 < x \leq 4\) - C. \(x = 0\) - D. None **Correct Answer: C** **Graph Explanation:** The graph is separated at \(x = 0\), where there is a clear break indicating a lack of continuity and differentiability. Elsewhere, the curve and line are smooth, indicating differentiability.
Transcribed Image Text:**Graph Analysis and Questions on Differentiability and Continuity** The figure on the left shows the graph of a function \( y = f(x) \) over the closed interval \(-2 \leq x \leq 4\). The function is depicted with blue lines and solid dots to indicate closed intervals and open dots for open intervals. **Graph Description:** - The graph consists of two segments. - The first segment ranges from \((-2, 0)\) to \((0, 2)\). - The second segment is a curve starting just after \((0, 2)\) and extends to \((4, -3)\). **Key Points:** - The function appears to be continuous and differentiable from \(-2 \leq x < 0\) and \(0 < x \leq 4\). - At \(x = 0\), the function appears to be neither continuous nor differentiable due to a break in the graph. **Questions:** a. **At what domain points does the function appear to be differentiable?** - A. \(-2 \leq x \leq 4\) - B. \(x = 0\) - C. \(-2 \leq x < 0, 0 < x \leq 4\) - D. None **Correct Answer: C** b. **At what domain points does the function appear to be continuous but not differentiable?** - A. \(-2 \leq x \leq 4\) - B. \(-2 \leq x < 0, 0 < x \leq 4\) - C. \(x = 0\) - D. None **Correct Answer: D** c. **At what domain points does the function appear to be neither continuous nor differentiable?** - A. \(-2 \leq x \leq 4\) - B. \(-2 \leq x < 0, 0 < x \leq 4\) - C. \(x = 0\) - D. None **Correct Answer: C** **Graph Explanation:** The graph is separated at \(x = 0\), where there is a clear break indicating a lack of continuity and differentiability. Elsewhere, the curve and line are smooth, indicating differentiability.
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