Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. (Select all that apply.) F(x) = { x ² + 1 if x # if x = 0 10- 5. +H -4-3-2-1 1 2 3 4 Ⓡ ✔The function f is discontinuous at x = 0 because f is not defined at x = 0. ✔The function f is discontinuous at x = 0 because lim f(x) does not exist. x+0 ✔The function f is discontinuous at x = 0 because lim f(x) exists, but this limit is not equal to f(0). ✔The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x. x
Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. (Select all that apply.) F(x) = { x ² + 1 if x # if x = 0 10- 5. +H -4-3-2-1 1 2 3 4 Ⓡ ✔The function f is discontinuous at x = 0 because f is not defined at x = 0. ✔The function f is discontinuous at x = 0 because lim f(x) does not exist. x+0 ✔The function f is discontinuous at x = 0 because lim f(x) exists, but this limit is not equal to f(0). ✔The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x. x
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 4ECP
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Ex 2.5 q12
Transcribed Image Text:Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. (Select all that apply.)
F(x) = { x ² + 1 if x #
if x = 0
10-
5.
+H
-4-3-2-1
1 2 3 4
Ⓡ
✔The function f is discontinuous at x = 0 because f is not defined at x = 0.
✔The function f is discontinuous at x = 0 because lim f(x) does not exist.
x+0
✔The function f is discontinuous at x = 0 because lim f(x) exists, but this limit is not equal to f(0).
✔The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x.
x
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