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."
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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![**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."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56488219-115f-4b7a-9fca-52b6982bead0%2F182f8a2e-e1be-49bb-a319-af6c3fb29a8d%2Fhma5mz_processed.jpeg&w=3840&q=75)
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."
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