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The graph of y = f(x) is shown. Use the graph to answer the question. Find 2; -2 lim x→0- f(x) and O -1,2 O 2, -1 O 2, does not exist O -2, -1 X lim X→0+ f(x).

The graph of y = f(x) is shown. Use the graph to answer the question. Find 2; -2 lim x→0- f(x) and O -1,2 O 2, -1 O 2, does not exist O -2, -1 X lim X→0+ f(x).

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 of y = f(x) The provided graph depicts the function \( y = f(x) \). Utilize this graph to respond to the following question. **Graph Description:** - The graph is divided into four quadrants by the x-axis (horizontal axis) and y-axis (vertical axis). - The graph consists of two separate lines. - The line in the second quadrant extends toward the origin (0, 0) and continues negatively towards the third quadrant. - The line in the first quadrant also heads towards the origin and continues positively into the first quadrant. - Both lines intersect the y-axis at \( y = -2 \) and \( y = 2 \) respectively. ### Question: Find \(\lim_{{x \to 0^-}} f(x)\) and \(\lim_{x \to 0^+} f(x)\). **Options:** - \( \text{A) } -1, 2 \) - \( \text{B) } 2, -1 \) - \( \text{C) } 2, \text{ does not exist} \) - \( \text{D) } -2, -1 \) **Analysis of the Graph:** As \( x \) approaches 0 from the left (\( x \to 0^- \)), the value of \( f(x) \) is moving towards -2. As \( x \) approaches 0 from the right (\( x \to 0^+ \)), the value of \( f(x) \) is moving towards 2. ### Correct Answer: - Answer: \( \text{A) } -2, 2 \)
Transcribed Image Text:### Graph of y = f(x) The provided graph depicts the function \( y = f(x) \). Utilize this graph to respond to the following question. **Graph Description:** - The graph is divided into four quadrants by the x-axis (horizontal axis) and y-axis (vertical axis). - The graph consists of two separate lines. - The line in the second quadrant extends toward the origin (0, 0) and continues negatively towards the third quadrant. - The line in the first quadrant also heads towards the origin and continues positively into the first quadrant. - Both lines intersect the y-axis at \( y = -2 \) and \( y = 2 \) respectively. ### Question: Find \(\lim_{{x \to 0^-}} f(x)\) and \(\lim_{x \to 0^+} f(x)\). **Options:** - \( \text{A) } -1, 2 \) - \( \text{B) } 2, -1 \) - \( \text{C) } 2, \text{ does not exist} \) - \( \text{D) } -2, -1 \) **Analysis of the Graph:** As \( x \) approaches 0 from the left (\( x \to 0^- \)), the value of \( f(x) \) is moving towards -2. As \( x \) approaches 0 from the right (\( x \to 0^+ \)), the value of \( f(x) \) is moving towards 2. ### Correct Answer: - Answer: \( \text{A) } -2, 2 \)
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