Problem

Sketch the graph of a function $ f $ that is cont…

01:31

Question

Answered step-by-step

Problem 7 Easy Difficulty

Sketch the graph of a function $ f $ that is continuous except for the stated discontinuity.

Removable discontinuity at 3, jump discontinuity at 5.

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Leon Druch

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Video Transcript

Okay, we want to sketch the graph of a function F of X. We want a removable dis continuity at three. And the jump just continuity at five. A removable dis continuity when x is straight. So let's have an open circle right here, at X equals tree. And here is the graph of our function As X is approaching three from the left side here is the graph of the function um as X is approaching three from the positive side. Now, let's define a function when X is three to be this point right here. All right. So this is what we would call a removable dis continuity at three. You can see that this function is discontinuous at three because as the function approach, as X approaches three, okay, to function looks like a once approach approach this point. This value here instead, the function is defined to be this value up here. Uh This is a removable dis continuity. If we redefined ffx when X equals three to be this point. If we move this point of the function and put it here, uh then we would have a continuous function. So that's why this is called a removable dis continuity. A jump. This continuity at five is a little more serious. Let's suppose. Um as x approaches five from the left, uh the function is approaching uh this point right here. So this will be the value of the functions when X equals five, but we're going to continue our function um up here with an open circle because if uh F five is this point here, then we can't have another point of the function for the same X value five. So, open circle meaning this is not really on the graph, but then from here on for X is greater than five. We're continuing to graph uh over there. So now that we have an idea what the graph looks like, let's look at it. We said that at X equals three. We have removable dis continuity. The function is discontinuous. You have a low breaking a function but this discount this this this continuity is removable because we can redefine f of X when X equals three. Instead of being this point, put it down here and it will be continuous here. We have what's called a jump dis continuity. There's no way to remedy this. Um here, as X approaches five, the function approaches this point here, but then as we continue on past five, uh function continues on on this portion of the graph up here. Clearly, the function is discontinued. Clearly, the function is discontinuous at X equals five and this is called a jump discontinuity because the graph of F. Quebec's jumped from here and then up to here to continue

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem