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-x-7 fres-2 [F(x)= x² for-2<152 fora > 2 At x = -2 because limit as x approaches -2 of f(x) Does Not Exist At x = 2 because limit as x approaches 2 of f(x) Does Not Exist At x = -2 because there is a hole in the graph At x = 2 because there is a hole in the graph At x = -2 because f(-2) Does Not Exist At x = 2 because f(2) Does Not Exist

-x-7 fres-2 [F(x)= x² for-2<152 fora > 2 At x = -2 because limit as x approaches -2 of f(x) Does Not Exist At x = 2 because limit as x approaches 2 of f(x) Does Not Exist At x = -2 because there is a hole in the graph At x = 2 because there is a hole in the graph At x = -2 because f(-2) Does Not Exist At x = 2 because f(2) Does Not Exist

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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**QUESTION 22** 20) Using the graph below, find to state ALL points where the function is discontinuous and WHY? _(Lecture Image Explanation)_ The provided graph shows a piecewise function \( f(x) \) which is defined as: - \( f(x) = -x^2 \) for \( x \leq -2 \) - \( f(x) = 3x + 2 \) for \( -2 < x \leq 2 \) - \( f(x) = 2 \) for \( x > 2 \) There is a visible hole (discontinuity) at \( x = -2 \) and \( x = 2 \) on the graph, where the pieces of the function do not connect smoothly. _Question’s Multiple Choice Options:_ A) At \( x = -2 \) because limit as \( x \) approaches -2 of \( f(x) \) Does Not Exist At \( x = 2 \) because limit as \( x \) approaches 2 of \( f(x) \) Does Not Exist B) At \( x = -2 \) because there is a hole in the graph At \( x = 2 \) because there is a hole in the graph C) At \( x = -2 \) because \( f(-2) \) Does Not Exist At \( x = 2 \) because \( f(2) \) Does Not Exist **Note:** From the graph, it is clear that the function \( f(x) \) has discontinuities at the points \( x = -2 \) and \( x = 2 \) due to holes in the graph. _Explanation of the Graph:_ - **Point \( x = -2 \):** The limit from the left as \( x \) approaches -2 is not equal to the limit from the right as \( x \) approaches -2 which causes a discontinuity. - **Point \( x = 2 \):** The function shows a jump in the graph at \( x = 2 \) where the pieces of the function do not connect smoothly, again creating a discontinuity.
Transcribed Image Text:**QUESTION 22** 20) Using the graph below, find to state ALL points where the function is discontinuous and WHY? _(Lecture Image Explanation)_ The provided graph shows a piecewise function \( f(x) \) which is defined as: - \( f(x) = -x^2 \) for \( x \leq -2 \) - \( f(x) = 3x + 2 \) for \( -2 < x \leq 2 \) - \( f(x) = 2 \) for \( x > 2 \) There is a visible hole (discontinuity) at \( x = -2 \) and \( x = 2 \) on the graph, where the pieces of the function do not connect smoothly. _Question’s Multiple Choice Options:_ A) At \( x = -2 \) because limit as \( x \) approaches -2 of \( f(x) \) Does Not Exist At \( x = 2 \) because limit as \( x \) approaches 2 of \( f(x) \) Does Not Exist B) At \( x = -2 \) because there is a hole in the graph At \( x = 2 \) because there is a hole in the graph C) At \( x = -2 \) because \( f(-2) \) Does Not Exist At \( x = 2 \) because \( f(2) \) Does Not Exist **Note:** From the graph, it is clear that the function \( f(x) \) has discontinuities at the points \( x = -2 \) and \( x = 2 \) due to holes in the graph. _Explanation of the Graph:_ - **Point \( x = -2 \):** The limit from the left as \( x \) approaches -2 is not equal to the limit from the right as \( x \) approaches -2 which causes a discontinuity. - **Point \( x = 2 \):** The function shows a jump in the graph at \( x = 2 \) where the pieces of the function do not connect smoothly, again creating a discontinuity.
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