**Graph Analysis:** The provided graph is of the function \( f(x) \) and is plotted on a coordinate plane. The x-axis ranges from -5 to 3, and the y-axis ranges from -2 to 5. The graph features: - A curve with an endpoint at x = -5 that heads toward negative infinity. - A peak at approximately \( x = -3 \) where \( f(x) = 4 \). - A sharp valley at \( x = -2 \) where the function continues. - A jump discontinuity at \( x = 1 \) where the graph jumps from \( f(1) = 2 \) to \( f(1) = 3 \). - An open circle at \( x = -3 \) and a solid point at \( x = 3 \), indicating a break in continuity. **Questions:** 1. **Evaluate the following, if possible. If not, write DNE and explain why not.** a. \(\lim_{x \to -\infty} f(x) = \) b. \(\lim_{x \to -3} f(x) = \) c. \(\lim_{x \to -2^+} f(x) = \) d. \(\lim_{x \to 1} f(x) = \) e. \( f'(2) = \) f. \( f'(-1) = \) 2. **On what interval of \( x \)-values is \( f \) continuous? Write your answer using correct set notation.** 3. **Identify the \( x \)-value(s) for which \( f \) is not differentiable. Write your answer using correct set notation.** This set of questions requires understanding of limits, continuity, and differentiability of functions. Review the graph carefully to determine where these properties hold or fail.
**Graph Analysis:** The provided graph is of the function \( f(x) \) and is plotted on a coordinate plane. The x-axis ranges from -5 to 3, and the y-axis ranges from -2 to 5. The graph features: - A curve with an endpoint at x = -5 that heads toward negative infinity. - A peak at approximately \( x = -3 \) where \( f(x) = 4 \). - A sharp valley at \( x = -2 \) where the function continues. - A jump discontinuity at \( x = 1 \) where the graph jumps from \( f(1) = 2 \) to \( f(1) = 3 \). - An open circle at \( x = -3 \) and a solid point at \( x = 3 \), indicating a break in continuity. **Questions:** 1. **Evaluate the following, if possible. If not, write DNE and explain why not.** a. \(\lim_{x \to -\infty} f(x) = \) b. \(\lim_{x \to -3} f(x) = \) c. \(\lim_{x \to -2^+} f(x) = \) d. \(\lim_{x \to 1} f(x) = \) e. \( f'(2) = \) f. \( f'(-1) = \) 2. **On what interval of \( x \)-values is \( f \) continuous? Write your answer using correct set notation.** 3. **Identify the \( x \)-value(s) for which \( f \) is not differentiable. Write your answer using correct set notation.** This set of questions requires understanding of limits, continuity, and differentiability of functions. Review the graph carefully to determine where these properties hold or fail.
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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Q7: Can you solve this question with showing your work clearly please write clearly so I can see your work and numbers. PLEASE answer all the parts to the question
Transcribed Image Text:**Graph Analysis:**
The provided graph is of the function \( f(x) \) and is plotted on a coordinate plane. The x-axis ranges from -5 to 3, and the y-axis ranges from -2 to 5. The graph features:
- A curve with an endpoint at x = -5 that heads toward negative infinity.
- A peak at approximately \( x = -3 \) where \( f(x) = 4 \).
- A sharp valley at \( x = -2 \) where the function continues.
- A jump discontinuity at \( x = 1 \) where the graph jumps from \( f(1) = 2 \) to \( f(1) = 3 \).
- An open circle at \( x = -3 \) and a solid point at \( x = 3 \), indicating a break in continuity.
**Questions:**
1. **Evaluate the following, if possible. If not, write DNE and explain why not.**
a. \(\lim_{x \to -\infty} f(x) = \)
b. \(\lim_{x \to -3} f(x) = \)
c. \(\lim_{x \to -2^+} f(x) = \)
d. \(\lim_{x \to 1} f(x) = \)
e. \( f'(2) = \)
f. \( f'(-1) = \)
2. **On what interval of \( x \)-values is \( f \) continuous? Write your answer using correct set notation.**
3. **Identify the \( x \)-value(s) for which \( f \) is not differentiable. Write your answer using correct set notation.**
This set of questions requires understanding of limits, continuity, and differentiability of functions. Review the graph carefully to determine where these properties hold or fail.
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