Question

Does the function represented by the graph have an inverse function? The three coordinates are (0,0), (4,8), and (8,0).

Answer 1

Plot all of the points. If you can draw a horizontal straight line through any two points, then this function fails the horizontal line test. Any time you fail the horizontal line test, the function won't have an inverse.

Answer 2

I cannot, because the line is slanted on the graph.

Answer 3

did you plot the three points?

Answer 4

yes. It's been drawn for me.

Answer 5

ok is it possible to draw a flat horizontal line through more than one point?

Answer 6

Yes, between zero and eight.

Answer 7

yeah through (0,0) and (8,0)

so this means the horizontal line test fails and we won't have an inverse function

Answer 8

Why? I think there should be an inverse. I just don't know the function for the graph.

Answer 9

did you learn about the vertical line test?

Answer 10

Not yet. We're talking about functions and graphs. Also domain and range.

Answer 11

well the rule about functions is that a relation must pass the vertical line test in order to be a function

Answer 12

if you can pass a vertical line through more than one point, then the vertical line test fails and we do NOT have a function

Answer 13

Ok. But how do I find the function of the graph?

Answer 14

In this case, we just have 3 points. It seems like there isn't enough information to find the actual function

Answer 15

can you post a screenshot of the full thing?

Answer 16

I will check my notes, but they're confusing.

Answer 17

I recommend watching this video about the vertical line test

https://www.youtube.com/watch?v=-xvD-n4FOJQ

hopefully it will help

Answer 18

I haven't learned that yet, so would it count if put the vertical and horizontal tests as my answer?

Answer 19

if you haven't learned it, then the teacher probably won't accept it. But it's handy to learn nonetheless (chances are the teacher will teach it later down the road)

Answer 20

I need the exact answer, because I have a test tomorrow and I never got a question like this before. I can find the inverse of a function if it's given.

Answer 21

can you post a screenshot of the full thing?

Answer 22

Ok. Sorry.

Answer 23

I cannot attach a picture.

Answer 24

the "attach file" button isn't working?

Answer 25

maybe host it on a site like imgur and then paste the link

Answer 26

I have instagram.

Answer 27

that might work, just as long as you can host the image somewhere and share the link

Answer 28

My username is princess5062. You can see the picture that I just uploaded.

Answer 29

https://instagram.com/p/7Ja6_CmGRgNTAiNKsvvsYhyWXzo4VLMRi9m1A0/?taken-by=princess5062

Answer 30

it's telling me "Sorry, this page isn't available"

Answer 31

you have to have an account. It worked when I was logged on.

Answer 32

oh sorry I don't have an account. There's no way to share to non-account holders?

Answer 33

maybe I should i create an imgur account

Answer 34

you don't need to create one, they allow you to upload without an account

Answer 35

thanks

Answer 36

Sorry, it took forever.

Answer 37

ok so it's a V shaped line, I see now

Answer 38

That's what I said like a parabola.

Answer 39

ok so the domain you have (0,8) is close but not quite there

the actual domain is [0,8]. What's the difference? The difference is that the endpoints are included when you use square brackets.

Answer 40

Oh. It's because my friend said that the brackets are for the range only. Ok, thank you for that. Can I use any information I wrote down for the function?

Answer 41

no, as long as there is a solid point on the graph, it is included. The endpoints have solid points (closed circles). if you saw open circles, then you would exclude those points

Answer 42

`Can I use any information I wrote down for the function?` I'm not sure what you mean

Answer 43

Like the average rate of change, can I put that in an equation that is the function of the graph?

Answer 44

oh, yes you can to describe the slope of each piece of the V shape

Answer 45

so for #3, you'll have 2 answers there

Answer 46

That's the average rate of change also known as slope.

Answer 47

I got 2 and -2 for the rate of change. There is an inverse, because the signs are the opposite.

Answer 48

yes for the first half from 0 to 4, the slope is +2
the second half from 4 to 8 has the slope -2

Answer 49

Is it going to be an equation or inequality?

Answer 50

the graph you mean?

Answer 51

Yes, the function of the graph.

Answer 52

the function is an equation

Answer 53

I thought it was an equality, because 2 and -2 are opposite of each other.

Answer 54

so the equation is y=|x| + 2 = -2?

Answer 55

equality is the same as equation
both have "equa" in them

an inequality is something like y > 2x which would involve shading

Answer 56

the vertex is at (4,8) so h = 4, k = 8
the value of 'a' is a = -2 because the V shape is stretched by a factor of 2. The negative is to mean "flip the V upside down"

y = a|x-h|+k
y = -2|x-4| + 8

is your equation

Answer 57

The function is not an equation with the letter y. We have to find the equation for the function.

Answer 58

you can replace y with f(x)

Answer 59

I might be wrong, because I looked at problem six, it's asking for an equation of the function.

Answer 60

yeah you start with y = |x| and do a bunch of transformations to end up with y = -2|x-4| + 8

Answer 61

Where did you get the eight?

Answer 62

that's the y coordinate of the vertex

Answer 63

Thank you. How did you get the equation? Sorry, I'm not understanding your equation.

Answer 64

I started with the template y = a|x-h|+k

Answer 65

have you learned about y = a|x-h|+k ?