Consider the following graph of a function f(x) 4 A. For what value(s) x is f discontinuous? If f is continuous everywhere, answer "none." Justify your answer using the conditions of continuity. B. For what value(s) x is f non-differentiable? If f is differentiable everywhere, answer "none." Justify your answer using the conditions of differentiability. C. What is lim f(x)? If the value does not exist, x-2 answer "DNE." D. What is lim f(x)? If the value does not exist, x→1 answer "DNE."
Consider the following graph of a function f(x) 4 A. For what value(s) x is f discontinuous? If f is continuous everywhere, answer "none." Justify your answer using the conditions of continuity. B. For what value(s) x is f non-differentiable? If f is differentiable everywhere, answer "none." Justify your answer using the conditions of differentiability. C. What is lim f(x)? If the value does not exist, x-2 answer "DNE." D. What is lim f(x)? If the value does not exist, x→1 answer "DNE."
Transcribed Image Text:**Consider the following graph of a function \( f(x) \)**
*[Graph Description]:*
The graph illustrates a function \( f(x) \) with the following distinct features:
1. On the interval to the left of \( x = 0 \), the function is a smooth curve that approaches \( y = -1 \) as \( x \) approaches -1.
2. There is a discontinuous point at \( x = 1 \), where the function has a hole in the curve and a defined point above it around \( y = 1 \). The rest of the curve on either side of this discontinuity seems to be continuous.
3. Between \( x = 2 \) and \( x = 3 \), the graph is continuous and follows a rational curve shape.
4. At \( x = 4 \), the function shifts to a piecewise linear segment forming a sharp corner, which is a hallmark of non-differentiability at that point.
**Questions and Instructions:**
A. For what value(s) \( x \) is \( f \) discontinuous? If \( f \) is continuous everywhere, answer "none." Justify your answer using the conditions of continuity.
B. For what value(s) \( x \) is \( f \) non-differentiable? If \( f \) is differentiable everywhere, answer "none." Justify your answer using the conditions of differentiability.
C. What is \( \lim_{{x \to 2}} f(x) \) ? If the value does not exist, answer "DNE."
D. What is \( \lim_{{x \to 1}} f(x) \) ? If the value does not exist, answer "DNE."
E. What is \( \lim_{{x \to 3}} f(x) \) ? If the value does not exist, answer "DNE."
F. What is \( f(2) \) ? If the value does not exist, answer "DNE."
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
![**Consider the following graph of a function \( f(x) \)**
*[Graph Description]:*
The graph illustrates a function \( f(x) \) with the following distinct features:
1. On the interval to the left of \( x = 0 \), the function is a smooth curve that approaches \( y = -1 \) as \( x \) approaches -1.
2. There is a discontinuous point at \( x = 1 \), where the function has a hole in the curve and a defined point above it around \( y = 1 \). The rest of the curve on either side of this discontinuity seems to be continuous.
3. Between \( x = 2 \) and \( x = 3 \), the graph is continuous and follows a rational curve shape.
4. At \( x = 4 \), the function shifts to a piecewise linear segment forming a sharp corner, which is a hallmark of non-differentiability at that point.
**Questions and Instructions:**
A. For what value(s) \( x \) is \( f \) discontinuous? If \( f \) is continuous everywhere, answer "none." Justify your answer using the conditions of continuity.
B. For what value(s) \( x \) is \( f \) non-differentiable? If \( f \) is differentiable everywhere, answer "none." Justify your answer using the conditions of differentiability.
C. What is \( \lim_{{x \to 2}} f(x) \) ? If the value does not exist, answer "DNE."
D. What is \( \lim_{{x \to 1}} f(x) \) ? If the value does not exist, answer "DNE."
E. What is \( \lim_{{x \to 3}} f(x) \) ? If the value does not exist, answer "DNE."
F. What is \( f(2) \) ? If the value does not exist, answer "DNE."](https://content.bartleby.com/qna-images/question/56488219-115f-4b7a-9fca-52b6982bead0/182f8a2e-e1be-49bb-a319-af6c3fb29a8d/hma5mz_processed.jpeg)
Thomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. Freeman
Calculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning