Question

Consider the following relation.

x=−4|y|+3

Find four points contained in the inverse. Express your values as an integer or simplified fraction.

Answer 1

@snowflake0531

Answer 2

What is the inverse function?

Answer 3

Switch x and y. What do you get?

Answer 4

y=−4|x|+3

Answer 5

There is no inverse

Answer 6

That is the inverse

Answer 7

Now find four points that are on that graph

Answer 8

i couldn't find them

Answer 9

Seems like you're struggling... you can replace x with any number and then solve for y.

And you'll then have the y-coordinate for that x-value and thus you have one point.

You then repeat the process

Answer 10

It's really simple.

Alternatively, you can just graph it and pick points from that: https://www.desmos.com/calculator/gozrhvd5jk

Answer 11

(0, 3), (1, -1), (2, -5) , (-1, 1)

Answer 12

the fourth point you listed should be (-1, -1)

Answer 13

(0, 3), (1, -1), (2, -5) , (-1, -1)

Answer 14

is that right in order ?

Answer 15

is that right in order ?

Answer 16

the order doesn't matter but all those points are valid

Answer 17

ok

Answer 18

Consider the following relation.

x= −4|y|+3

Find the domain and range of the inverse. Express your answer in interval notation.

Answer 19

@tranquility

Answer 20

Look at the graph. What are the possible x-values?

What are the possible y-values?

Answer 21

well the previous answer was (0, 3), (1, -1), (2, -5) , (-1, 1)

Answer 22

can x be 100? can it be 1000?

Answer 23

can it be -100?

Answer 24

sure

Answer 25

so then you would say the domain (or the possible x-values for the graph) is from negative infinity to positive infinity

Answer 26

What about the range?

Is there a certain value that the y-coordinate can't be?
Look at the graph to find it

The range is going to be all numbers (that's less than that number) to negative infinity

Answer 27

5/4

Answer 28

No

Answer 29

What is the largest possible y-value

Answer 30

0,3

Answer 31

So... what is the maximum y-value of the equation?

Answer 32

x

Answer 33

that doesn't look like a number to me

Answer 34

The y-values are on the y-axis

can the y-value ever be 4?

Answer 35

yes

Answer 36

No.

Answer 37

oh i just checked over, no it couldn't from that row

Answer 38

So what is the maximum y value?

Answer 39

What is the range going to be?

What are the possible y-values

Answer 40

1 or -1

Answer 41

... that doesn't seem like a range of possible values for the y-value

Answer 42

Can the y-value be 5?

Can it be 4?

Can it be 3?

Can it be 2?

Can it be 1?

Can it be 0?

Can it be -100?

Answer 43

it can be 5

Answer 44

look at the graph again and again

Answer 45

can the y-value EVER be 5?

Answer 46

oh no

Answer 47

it seems on the graph could be 0 or 2 to me if i'm not mistaken

Answer 48

the y-value can be ANYTHING less than 3

Answer 49

Or

Answer 50

okay, i could go with 1 instead

Answer 51

the y-value can be 3 when x is 0

the y-value can be 0 when x is 0.75 or -0.75

the y-value can be -5 when x is 2 or -2

Answer 52

oh sorry , see i wasn't much good with math and it's been a while so it kind've has to flow back into my memory

Answer 53

You need to review a lot of basics

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/introduction-to-interval-notation

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/domain-of-a-function-intro

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/range-of-a-function

Answer 54

Excuses won't help you learn

Answer 55

I get it

Answer 56

You watched all three videos in less than 2 minutes?

Answer 57

I meant what you said

Answer 58

ok i seen them

Answer 59

can we go back to the question and finally solve it ?

Answer 60

I doubt you watched them but sure

So what's the answer?

Answer 61

I've already told you the answers

Answer 62

Nope

Answer 63

Is that all the possible y-values?

Is that how you write it in interval notation?

Answer 64

So far, that is not all the possible y values has to be defined

and No

Answer 65

Watch the videos first. It'll help you understand the concepts and will help you on the rest of your questions because it's the same concept again and again.

I've tried my best explaining it through text but obviously it wasn't good enough. Maybe the video will be easier to understand

Answer 66

I understand a little bit of it now

Answer 67

It demonstrates to find the domain, you would have to find the domain from left to right and the range starts from up and down. Correct ?

Answer 68

Domain: 3

Answer 69

@tranquility

Answer 70

oh sorry

Answer 71

ok first , 0 would be the only maximum value

Answer 72

The domain by the point seems to be : 0, 3

right or wrong

Answer 73

The domain by the point seems to be : 0, 3

right or wrong

Answer 74

the domain is a range of numbers that can be possible from left to right

Answer 75

Basically when you look at the graph, it keeps extending downwards

you could plug in x = 10000 and you would get a y-value for it

you could plug in x = -10000 and you would get a y-value for it

Answer 76

Oh my mistake , i mistaken that from the Range

Answer 77

since x can be any possible number on the number line, you say that the domain is all real numbers

Answer 78

Do you know how you would write that in interval notation?

Answer 79

yes i think so , I believe like this

\[(\infty, 3)\]

Answer 80

That is interval notation but not how you would write it

Since it can be any number, it's going to be from negative infinity to positive infinity

We are not stuck at x being equal to 3 because x can be equal to 4, 5, 6, 7.... any number all the way to infinity

so

\( (- \infty, \infty)\)

Answer 81

Oh and look , my apologizes for making you frustrated when you tried to explain it to me and showing me the videos . I have gained a little by little insight by the domain and range and now you put it in a way that all by real numbers by the x can be defined in any number,

Answer 82

Now , for the range i almost had off the tip of my tongue but i could be wrong

Answer 83

No worries! I hope you're learning something :)

Answer 84

For the range, you want to look from top to bottom

As we said, the graph would keep continuing downwards all the way to negative infinity.
And it begins at 3

So how would you write in interval notation that the range goes from 3 to negative infinity

Answer 85

Remember, since the 3 is included we have to use ] instead of ) for that side of the interval notation

Answer 86

\[(-\infty , 3]\]

Answer 87

Good job!

Answer 88

Alright , thank you sir and i'll still keep learning.

Answer 89

No problem