Question

New question.

Answer 1

Find the domain and range of a cubic function.

Answer 2

I cant draw :/

Answer 3

What are you trying to draw?

Answer 4

Function and my solution to the problem

Answer 5

Seems like operator error to me

Answer 6

Is that a roast?

Answer 7

I know you told me this method only works for even root functions but i just wanted to see what happens :)

Answer 8

I did plugin f(-3) and it gave me a positive y value

Answer 9

Except it is a cubic function. I told you that the method I showed you is only useful for EVEN roots

Answer 10

3 is clearly odd

Answer 11

I know...i remember.. but i just wanted to test the water u know

Answer 12

Test it with even roots

Answer 13

Got it lol

Answer 14

Is there an easier method to find the domain of a cubic function?

Answer 15

Everything rule I tell you, you find a way to violate. I'm clearly getting a preview of what it will be like having kids.

Answer 16

Yes, there is an easier way. It's called "look at that graphing chart I gave you".

Answer 17

Jesus pieces....why so mad :/ i was jus fiddling with numbers tho :/

Answer 18

I guess I have to follow up statements like that with *Humorous Tone* to ease your mind

Answer 19

Did you figure it out yet?

Answer 20

I drew you the behaviour of an odd function...

Answer 21

With 3rd degree

Answer 22

Yeah but did you figure out the domain and range?

Answer 23

of the CUBIC Function

Answer 24

Looking at the parent function of a cubic function, the range should be *all real values are element of y* since there’s no restriction/asymptote..

Answer 25

Ah but you're overlooking the SQUARE

Answer 26

What happens when a negative number is squared?

Answer 27

Since the leading degree is 3, the square shouldn’t effect that much...i think

Answer 28

What is (-3)^2?

Answer 29

Becomes positive

Answer 30

Exactly, so what does that mean for the range?

Answer 31

That’s what i said earlier... there’s no restriction...i can plugin any value of x into the function and i’ll Always get a positive result

Answer 32

Wait hold up.... lol

Answer 33

There's no restriction on the RANGE? smh

Answer 34

Any negative value of x is turned positive with that square inside the cube root....i’m Always getting a positive result..but wait there’s a limit to the range

Answer 35

Exactly. Now we have to figure out what that limit is.

Answer 36

What do we know about the output of \(y = x^2\)

Answer 37

It is squared..

Answer 38

I'll ask this way, what do we know about the sign of the output value of \(y = x^2\)?

Answer 39

It’s positive

Answer 40

Most specifically, y will always be greater than or equal to zero

Answer 41

Oh i see... the resultant has to be positive

Answer 42

Wait, i have a side question here...can you take the cube root of a negative integer ?

Answer 43

Okay, I'm going to introduce you to a new method of finding the range of a cubic function. If you can handle it

Answer 44

To find the range of a cubic function algebraically, you have to find the inverse of the function.

Answer 45

And then domain of the inverse is the range of the function.

Answer 46

But it has to be short tho....

Answer 47

And the answer to your question is YES you can take the cube root of a negative number

Answer 48

So what does that tell you about the domain of a cubic function?

Answer 49

All real numbers?

Answer 50

Correct!

Answer 51

Now, back to finding the range. I'm going to walk you through this step by step.

Answer 52

Plz make it short tho :/

Answer 53

It's not long if you don't mess up.

Answer 54

First set y in place of \(f(x)\)

Answer 55

Show your work

Answer 56

Let me draw.

Answer 57

What do i do next ?

Answer 58

Next swap the x and y values

Answer 59

Very good, now isolate \(y\)

Answer 60

Wait, i need a hint... how do i get rid of the rational power again? Take cube root to both sides?

Answer 61

The cube is already a root

Answer 62

You should express the function as such

Answer 63

You need to express \(y = (x - a)^{m/n}\) as \(y = \sqrt[n]{(x - a)^m}\)

Answer 64

Then you should know what to do afterwards.

Answer 65

I got it... one second...

Answer 66

Nope, incorrect.

Answer 67

One second...

Answer 68

Still incorrect. Look at the formula above again before doing any work

Answer 69

Okie dokie

Answer 70

Wait, am i close tho?

Answer 71

I can't say

Answer 72

Just look at the formula. Pay closer attention to where the root is

Answer 73

Boom, there you go

Answer 74

You should know what to do next

Answer 75

Do i ? Wait.

Answer 76

I need a hint

Answer 77

Cube both sides.

Answer 78

Cube is the inverse of cube root so they cancel.

Answer 79

You did not cube both sides.

Answer 80

That's not how you cube both sides. You must have been playing games on your smartphone during Algebra. You don't seem to know how to do any Algebra.

Answer 81

I’m trying ;/

Answer 82

Nope that's not "cubing". You should research what it means to cube both sides of an equation. I have a question. What does it mean to square both sides of an equation?

Answer 83

Can you show an example?

Answer 84

It’s like dividing both sides by 1

Answer 85

No, it isn't

Answer 86

Wait, one second let me go watch a quick video.. brb

Answer 87

Squaring both sides of an equation (basic algebra btw)

Answer 88

Oh that.... smh..

Answer 89

Knowing that, what happens if you cube both sides of the equation?

Answer 90

Of the equation we're currently working on..

Answer 91

Is that it?

Answer 92

Actually you missed a step let me point it out: Somehow the 2 disappeared

Answer 93

I copied the wrong image... smh

Answer 94

Oh wait hang on

Answer 95

I think I was looking at your work wrong again.

Answer 96

You did it right the first time. Sorry

Answer 97

I jumped when I saw the two missing but you applied the square root to both sides which is correct

Answer 98

Very good. So now..... what is the domain of that function?

Answer 99

I solved for the y, just as you asked me to..what do i do next?

Answer 100

Did you read anything that I posted? Scroll up

Answer 101

I dont know the domain...:/

Answer 102

I'm out. Maybe @Ferredoxin4 can continue from here.

Answer 103

Aww sorry hero :/ i feel bad now :/

Answer 104

Let me see the question
just a moment

Answer 105

Hold on, I have to go for a bit, i'll be back in a few

Answer 106

@Ballery1 what did I say to do when you have an expression under a square root?

Answer 107

You need to apply something to find the domain of the function

Answer 108

We were just talking about negative numbers under a square root. What happens if you have a negative under a square root?

Answer 109

It becomes positive...

Answer 110

If you have a NEGATIVE under square root. Can you input that into your calculator? what is the square root of -1?

Answer 111

smh. I thought you graduated from this already

Answer 112

Omg...wait... undefined

Answer 113

So the value under the square root must be what?

Answer 114

It must be equal or bigger than -1

Answer 115

Not quite

Answer 116

No it must be bigger than -1

Answer 117

I get it now. It should be easy to get the domain from here..

Answer 118

The value under the square root must be greater than or equal to zero.

Answer 119

Yuhh... sq root of 0 is just 0... so it has to be bigger than 0

Answer 120

So set the expression under the square root to be greater than or equal to zero to find the domain of that function. When you find that, then you will have the range of the original function

Answer 121

I get it.. thank you sooooo much hero. You’re a real life hero :)

Answer 122

I know you think you got it, but I'd like to see the work.

Answer 123

I’ll post it in a second.

Answer 124

Brb :) let me write out everything, i’ll Post the answer in a but :)

Answer 125

Your typos are extrapolating.

Answer 126

Every single one of them involves some sexual reference.

Answer 127

What did i do now? :O

Answer 128

I'm just stating the trend I'm observing

Answer 129

I can list them if you like

Answer 130

I meant *a bit*

Answer 131

I swear it was an accident:/

Answer 132

I'm stating it so that you know that I know. That way if it happens again, there won't be any more excuses left for you to defend yourself against actions taken against your account.

Answer 133

Three accidents over 24 hours all involving the same offense.

Answer 134

It was an accident the first time

Answer 135

Ok i’m Sorry. I just want help with math, that’s all.

Answer 136

I just want to say that I'm happy to help you, but we have to be a little strict in terms of language usage since this is an educational site and we're still trying to grow. We have to set an example for newer members so that they know how to behave on the site. You being an a previous member of OS should already know how we operate. I don't recall reprimanding you on OS regarding behavior or usage.

Answer 137

Ok i have a question.

Answer 138

We're treating this environment in the same manner as if one was in a real classroom environment with active instruction taking place

Answer 139

It has to be outside the root since the square root is being applied to the \(x^3\) only

Answer 140

That’s what i thought... so when i plugin 0 into the root, i get 2. Ok

Answer 141

It is not part of the root when finding the inverse.

Answer 142

So what is the range of the function?

Answer 143

The lower limit is 0, and the upper limit is infinite

Answer 144

Correct. I highly recommend reviewing domain and range in IXL

Answer 145

What’s IXL again?

Answer 146

Extra large?

Answer 147

Remember the site you had difficulty seeing the images?

Answer 148

Oh that... okie dokie.

Answer 149

And the domain is x has to be equal or bigger than 0.

Answer 150

I think we focused so much on the range you forgot what the domain is.

Answer 151

We did go over it briefly already

Answer 152

Oh it has to be a positive integer

Answer 153

The question you must ask yourself is are there any restrictions on x? If so, what are they. In other words find the set of x values such that when you evaluate them in the function, gives an invalid or undefined output.

Answer 154

So the domain should be x has to be equal or greater than 0 right because when i plugin 0, i get 2. And the rest of the x values are defined and bigger and bigger

Answer 155

What happens if you plug in negative values for x?

Answer 156

Have you tried plugging them in?

Answer 157

I get an undefined ...

Answer 158

For what function?

Answer 159

When i plugin -1, i get undefined

Answer 160

You need the domain of the ORIGINAL function

Answer 161

Omg... that’s why... smh

Answer 162

The goal is to find the domain and range of the original function.

Answer 163

The work we did for the inverse was only to find the domain of the inverse to find the range of the ORIGINAL function.

Answer 164

Ah i see now.

Answer 165

It is important to keep track of what you're doing and for what purpose. Always have the goal in mind.

Answer 166

https://i.imgur.com/lI3qgH8.jpg

Answer 167

So how do we go about find the domain of the function?

Answer 168

You may want to make a template for yourself that has the following for every problem you do:

1. State the Problem
2. State the Goal
3. State the relevant concepts
4. State the plan (how do you plan to solve the problem)
5. Break your work into major parts (A, B, C):
A representing the first major step
B representing the next major step
C representing the third major step
...
And so on until you've solved the problem.

Then end with a concluding statement.

Answer 169

This is how you stay organized while doing mathematics.

Answer 170

It's how you avoid losing track

Answer 171

The domain of the inverse is the range of the original function. Repeat that 100 times to yourself

Answer 172

I’ll write that down on top of the paper. And yes

Answer 173

But write down that template and apply it to every problem you do

Answer 174

Did u mean to say *don’t* or *do*?

Answer 175

Write down that template and apply to every problem you work on.

Answer 176

Yes sir. Got it

Answer 177

For example: You were given \(f(x) = (x - 2)^{2/3}\) and asked to find domain and range so here's what I would do on paper:

Answer 178

I literally wrote down the steps to ffind the range of the original function using the inverse method.

Answer 179

So how do we go about finding the domain of the original function?

Answer 180

1. Given: \(f(x) = (x - 2)^{2/3}\)
2. Find domain and range
3. The domain of the function is the set of valid x values of f(x)
The range is the set of all valid y values of f(x)
4. To find the domain of a function, in general, I must first consider any restrictions on x. If there are any restrictions on x, I must exclude it from the domain.
To find the range of the cubic function I must find the inverse of the original function then find the domain of the inverse function. The domain of the inverse function will be the range of the original function.

A. Work to Find domain of the given function is as follows:

..... then post your work


B. Work to Find Range of the given function is as follows:

.....post that work


C. Conclusion: The domain is ..., The range is ...

Answer 181

If you deviate from this, you'll have problems such as losing track of where when and what

Answer 182

The template saves you from confusion. You'll always know what is going on if you follow this.

Answer 183

Even if you get lost, you'll know exactly where you are lost rather than just being lost and having no clue at all

Answer 184

Thank you for posting the steps

Answer 185

Ok now that we’ve found the range of the original function using the inverse method, shall we continue to find the domain of the function?

Answer 186

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Hero
To find the domain, The question you must ask yourself is are there any restrictions on x? If so, what are they. In other words find the set of x values such that when you evaluate them in the function, gives an invalid or undefined output.
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 187

Yes, let me plugin some values into the original function and see

Answer 188

Oops, my pencil died...one second plz :)

Answer 189

So what does this tell you in terms of the domain? Did you get "invalid" or "undefined" when you evaluate negative numbers?

Answer 190

The domain is all real values

Answer 191

Bingo

Answer 192

I really appreciate your effort and time :)

Answer 193

You're welcome = yw

Answer 194

Ok :)

Answer 195

I was just kidding in the chat.

Answer 196

mkay

Answer 197

Ok let me write out everything and i’ll Post the next question *in a bit*.

Answer 198

Thanks :)

Answer 199

Actually I'm offically done for the day. I barely started on my own work. Let's see what you can do with the template method

Answer 200

Yeah... don’t come back until you finish your own homework. I’ll post my answers here

Answer 201

Thanks tho :)