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3. Identify all of the discontinuities that exist for each of the following functions: a) y=x+3)(x+2)(x-4) b) y 2(x+3) (x+4)(x+3) c) y = (3x+1) (x+4)

3. Identify all of the discontinuities that exist for each of the following functions: a) y=x+3)(x+2)(x-4) b) y 2(x+3) (x+4)(x+3) c) y = (3x+1) (x+4)

Calculus: Early Transcendentals
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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(3 marks) 3. Identify all of the discontinuities that exist for each of the following functions: ach) (3x+ 1) 2(x+3) (x+4)(x+3) c) y a) y = (x+3)(x+2)(x-4) b) y (x+4)
Transcribed Image Text:(3 marks) 3. Identify all of the discontinuities that exist for each of the following functions: ach) (3x+ 1) 2(x+3) (x+4)(x+3) c) y a) y = (x+3)(x+2)(x-4) b) y (x+4)
Expert Solution
Step 1

A function is said to be dis continuous if there is a gap in the graph of the function. Some discontinuities are removable while others are non-removable. There is also jump discontinuity.

Basically we can say if Denominator is zero function is discontinuous .so check when denominator is zero.

1)

y=1(x+3)(x+2)(x-4)let (x+3)(x+2)(x-4)=0⇒(x+3)=0,(x+2)=0,(x-4)=0x=-3,-2,4

Therefore function is discontinuous ate x=-3,-2,4

2)y=2(x+3)(x+4)(x+3)y=2(x+4)let (x+4)=0⇒x=-4

Therefore function is discontinuous ate x=-4

3)

y=(3x+1)(x+4)let (x+4)=0x=-4

Therefore function is discontinuous ate x=-4

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