Question

i can solve these questions myself but i need a proper method to do these piecewise functions.

Answer 1

determine the value of *x*, if any, at which each function is discontinues.

Answer 2

@Hero

Answer 3

we starting from basics firsts.

Answer 4

Do you have any ideas on this?

Answer 5

i can plugin some values for x and see. i do know that when x= 3, the function is zero

Answer 6

But does that mean it is "discontinuous"? at x = 3?

Answer 7

i mean i have a linear function and a point given

Answer 8

no

Answer 9

In order for the function to be discontinuous, there must be at least one value x for which f(x) is undefined.

Answer 10

AAh icy

Answer 11

i guess no ?

Answer 12

Correct, there is no value of x for which f(x) is undefined.

Answer 13

That's what discontinuous means. Discontinous function means that f(x) is "interrupted" at some point between \((-\infty, \infty)\)

Answer 14

because i can plugin infinite x values for the first function. and same goes for the second point as well...it'll make a weird horizontal line

Answer 15

Correct. No matter what x value you put into f(x), it will always generate an output value.

Answer 16

so how do i show my work tho?

Answer 17

i literally dont have any examples to copy off this question from

Answer 18

Basically, here's what you say:

Answer 19

all it says in the back of the book is *x=0* for the answer to that question

Answer 20

No, it's not true. They're trying to say the function is discontinuous at x = 0

Answer 21

sooo what do i do then?

Answer 22

But if what you wrote is correct, the function is still continuous.

Answer 23

Do me a favor, can you provide a screenshot of the problem from your book or computer?

Answer 24

let me rewrite the question...

Answer 25

u doubt me bro?

Answer 26

No, I just want to see how the book wrote it

Answer 27

ok one second plz

Answer 28

Ah okay, sorry I completely botched this question.

Answer 29

The correct answer is x = 0

Answer 30

To determine if a function is discontinuous, you have to apply the "Pencil rule"

Answer 31

You start from the left and then trace over the function with a pencil. The moment you have to pick the pencil up to start again with the next interval is where the function is discontinous. And that is at x = 0

Answer 32

So I practically gave you the write-up to this one in my previous two comments.

Answer 33

https://www.desmos.com/calculator

Answer 34

i've never done the pencil rule before. :/

Answer 35

You can't just post the link for desmos because it has to be a unique link in order to display the graph.

Answer 36

The pencil rule is not difficult. You apply it exactly as I have described.

Answer 37

But let me post the graph

Answer 38

https://www.desmos.com/calculator/pxpoduobx3

Answer 39

https://www.geogebra.org/classic/z8sxutxe

Answer 40

The way I have graphed it is the correct graph

Answer 41

Maybe you'll understand better now.

Answer 42

AAAAAAAAAA icy now

Answer 43

Geogebra is better than Desmos anyways

Answer 44

bro, how do i show my solution algebraically tho?

Answer 45

You can't show it algebraically. You can describe it as I did above though.

Answer 46

but can i do this tho?? wait

Answer 47

You can't show "lifting up a pencil" unless you post a video of yourself drawing it and then lifting up the pencil

Answer 48

But you can graph it by hand and show that it is discontinuous that way.

Answer 49

Well, even if you did it this way, each point is discontinuous from the other point. You'd have to plot the points in between the points infinitely which is not possible.

Answer 50

There is no practical algebraic solution. The best way to describe what is happening is using sentences to describe the pencil method.

Answer 51

k i'll just verbally explain the method and use each equation to plot the points to show a proof

Answer 52

thanks bro

Answer 53

There's one other thing you can do though.

Answer 54

vat?

Answer 55

But it still involves showing graphically.

Answer 56

thats k

Answer 57

i'm willing to draw the graph

Answer 58

ight thanks mate.

Answer 59

https://study.com/academy/lesson/discontinuous-functions-properties-examples-quiz.html

Answer 60

wow do u have a premium account with study.com?

Answer 61

i need to make notes for calc 1 and linear alg

Answer 62

it tells me to register to view the whole video

Answer 63

Ah I see. I didn't realize it.

Answer 64

do u have a subscription to a math site?

Answer 65

i could use some help :/

Answer 66

I could have sworn I gave you ixl

Answer 67

bro i never really used it cuz i changed my mind on this program like 90 times

Answer 68

What program?

Answer 69

network eng

Answer 70

Oh you're still doing that

Answer 71

bruhh i haven't even started

Answer 72

I bet

Answer 73

You should do something you're actually interested in that you can actually finish.

Answer 74

im scared, i know i can do it but i'm afraid at the same time

Answer 75

Just pretend you're chinese.

Answer 76

They finish everything faster than we do and fear nothing.

Answer 77

i like networking. i think it's amazing...it's just the maths and physics that's getting in my way

Answer 78

Yup

Answer 79

so yeah.. i wanna make notes for math courses fast so i can move on with other stuff

Answer 80

You don't need study.com to take notes.

Answer 81

Just do it with Khan Academy

Answer 82

like coding, programming, networking ..uhg

Answer 83

There's a way to get an archive of all the videos without having to do the lessons.

Answer 84

but he does baby lotion soft questions and my textbook is diamond hard...it'll be no use for me

Answer 85

Which book are you studying

Answer 86

the one prof made for us /.-

Answer 87

Damn

Answer 88

yeah.... lol

Answer 89

Those are the worst ones

Answer 90

literally no freking solutions to questions or proper examples...i swear these teachers are so lazy

Answer 91

But what is the isbn?

Answer 92

Every book has an isbn

Answer 93

Can't be published without it

Answer 94

there's no isbn on this book....or at least that's what i think...the bar code is nearly erased....let me post

Answer 95

You can find the isbn on the back of the title page toward the very front of the book. Like within the first 3-5 pages

Answer 96

Wow I've never seen that before.

Answer 97

It's not published properly. Has a copyright but no ISBN

Answer 98

Yep, good luck.

Answer 99

bro, send me the website thingy

Answer 100

You should drop out and find a school where you can have access to better resources to help you. That school is trying to limit you with all kinds of restrictions. Might as well be a prison

Answer 101

I can find a link to khan academy's videos but it will take some time.

Answer 102

bro :/

Answer 103

What do you want?

Answer 104

can i have link to the math site you use with subscription plz : )

Answer 105

plz plz plz plz

Answer 106

i lost the link u gave me :/

Answer 107

But don't sleep on Khan Academy. It's the general concepts that he is great with explaining.