Determine if each function is continuous. If the function is not continuous, find the x-axislocation of and classify each discontinuity.1) f(x) =%3Dx2 - 2x + 1A) ContinuousC) Jump discontinuity at: xB) Essential discontinuity at: x = 1D) Removable discontinuity at: x = 0Essential discontinuity at: x =-13(-x² – 2x – 2, x<-12) f(x)= {xx2-112A) Removable discontinuity at: x =-2C) Essential discontinuity at: x = 3B) ContinuousD) Jump discontinuity at: x = -1S-x² + 2, x + 23) f(x) =1-3,x = 2A) Essential discontinuities at: x =-1, x = 0B) Removable discontinuity at: x = 2D) ContinuousC) Removable discontinuity at: x = 3[3,(2x + 3, x > -1xS-14) f(x) =A) Jump discontinuity at: x =-1B) Removable discontinuity at: x = 3Essential discontinuity at: x = 0C) Removable discontinuity at: x= 3Essential discontinuity at: x = -3D) Continuous5) f(x) = x³ – x² + 1A) Removable discontinuity at: x = -3B) Removable discontinuity at: x =-1Essential discontinuity at: x = 1D) Jump discontinuity at: x = -3C) Continuous< >

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Answered: 5) f(x) = x³ – x² + 1 B) Removable…

5) f(x) = x³ – x² + 1 B) Removable discontinuity at: x =-1 Essential discontinuity at: x = 1 A) Removable discontinuity at: x =-3 C) Continuous D) Jump discontinuity at: x = -3

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Determine if each function is continuous. If the function is not continuous, find the x-axis
location of and classify each discontinuity.
1) f(x) =
%3D
x2 - 2x + 1
A) Continuous
C) Jump discontinuity at: x
B) Essential discontinuity at: x = 1
D) Removable discontinuity at: x = 0
Essential discontinuity at: x =-1
3
(-x² – 2x – 2, x<-1
2) f(x)= {x
x2-1
12
A) Removable discontinuity at: x =-2
C) Essential discontinuity at: x = 3
B) Continuous
D) Jump discontinuity at: x = -1
S-x² + 2, x + 2
3) f(x) =
1-3,
x = 2
A) Essential discontinuities at: x =-1, x = 0
B) Removable discontinuity at: x = 2
D) Continuous
C) Removable discontinuity at: x = 3
[3,
(2x + 3, x > -1
xS-1
4) f(x) =
A) Jump discontinuity at: x =-1
B) Removable discontinuity at: x = 3
Essential discontinuity at: x = 0
C) Removable discontinuity at: x= 3
Essential discontinuity at: x = -3
D) Continuous
5) f(x) = x³ – x² + 1
A) Removable discontinuity at: x = -3
B) Removable discontinuity at: x =-1
Essential discontinuity at: x = 1
D) Jump discontinuity at: x = -3
C) Continuous
< >

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