Determine if the given function is continuous at the given number a. If it is discontinuous at a, determine if the discontinuity is removable or essential. Determine if the given function is continuous at the indicated number a. If it is discontinuous ata, determine if the discontinuity is removable or essential.1+ x, x<-2-2 < x< 2 (i)at x = 2, and (ii)at x = 22х — 1, х > 21. Н (х) %3D 32— х,у, у<12, y = 1 ;at y = 1(2у — 1, у>12. J(y) = :(2y + 1,3. G(y) = } 1-1sys1;at y = 1ży? - 3, 1

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a, determine if the discontinuity is removable or essential. 1+ x, x<-2 -2 2 1. H(x) = }2 – x,

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

Determine if the given function is continuous at the given number a. If it is discontinuous at a, determine if the discontinuity is removable or essential.

Determine if the given function is continuous at the indicated number a. If it is discontinuous at
a, determine if the discontinuity is removable or essential.
1+ x, x<-2
-2 < x< 2 (i)at x = 2, and (ii)at x = 2
2х — 1, х > 2
1. Н (х) %3D 32— х,
у, у<1
2, y = 1 ;at y = 1
(2у — 1, у>1
2. J(y) = :
(2y + 1,
3. G(y) = } 1
-1sys1
;at y = 1
ży? - 3, 1<y< 4
(x³ + 5x
4. f(x) = { x+ 2 °
if x + -2; at x = -2
-12, if x = -2
х — 2
(x + 1)(x – 2)
5. h(x) =
; at x = -1
4 - x2
6. f(x) =
at x = 2
3 - Vx² + 5;
7. Let g be defined by
(V7x +2 – Váx + 4
g(x) =
2
-.if x 2 -; and x # 2
х — 2
k, if x = 2
For what value of k is g a continuous function at x = 2?
8. For what values of m and b is J, defined by
-2, if x <3
J(x) = {mx + b, if 3 < x < 5
4, if 5 <x
Continuous at x = 3 and x = 5?

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