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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.
I cannot, because the line is slanted on the graph.
did you plot the three points?
yes. It's been drawn for me.
ok is it possible to draw a flat horizontal line through more than one point?
Yes, between zero and eight.
yeah through (0,0) and (8,0) so this means the horizontal line test fails and we won't have an inverse function
Why? I think there should be an inverse. I just don't know the function for the graph.
did you learn about the vertical line test?
Not yet. We're talking about functions and graphs. Also domain and range.
well the rule about functions is that a relation must pass the vertical line test in order to be a function
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
Ok. But how do I find the function of the graph?
In this case, we just have 3 points. It seems like there isn't enough information to find the actual function
can you post a screenshot of the full thing?
I will check my notes, but they're confusing.
I recommend watching this video about the vertical line test https://www.youtube.com/watch?v=-xvD-n4FOJQ hopefully it will help
I haven't learned that yet, so would it count if put the vertical and horizontal tests as my answer?
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)
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.
can you post a screenshot of the full thing?
I cannot attach a picture.
the "attach file" button isn't working?
maybe host it on a site like imgur and then paste the link
I have instagram.
that might work, just as long as you can host the image somewhere and share the link
My username is princess5062. You can see the picture that I just uploaded.
it's telling me "Sorry, this page isn't available"
you have to have an account. It worked when I was logged on.
oh sorry I don't have an account. There's no way to share to non-account holders?
maybe I should i create an imgur account
you don't need to create one, they allow you to upload without an account
Sorry, it took forever.
ok so it's a V shaped line, I see now
That's what I said like a parabola.
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.
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?
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
`Can I use any information I wrote down for the function?` I'm not sure what you mean
Like the average rate of change, can I put that in an equation that is the function of the graph?
oh, yes you can to describe the slope of each piece of the V shape
so for #3, you'll have 2 answers there
That's the average rate of change also known as slope.
I got 2 and -2 for the rate of change. There is an inverse, because the signs are the opposite.
yes for the first half from 0 to 4, the slope is +2 the second half from 4 to 8 has the slope -2
Is it going to be an equation or inequality?
the graph you mean?
Yes, the function of the graph.
the function is an equation
I thought it was an equality, because 2 and -2 are opposite of each other.
so the equation is y=|x| + 2 = -2?
equality is the same as equation both have "equa" in them an inequality is something like y > 2x which would involve shading
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
The function is not an equation with the letter y. We have to find the equation for the function.
you can replace y with f(x)
I might be wrong, because I looked at problem six, it's asking for an equation of the function.
yeah you start with y = |x| and do a bunch of transformations to end up with y = -2|x-4| + 8
Where did you get the eight?
that's the y coordinate of the vertex
Thank you. How did you get the equation? Sorry, I'm not understanding your equation.
I started with the template y = a|x-h|+k
have you learned about y = a|x-h|+k ?
Did you multiply 2 and -2?
I haven't learned that yet.
I did, I'm so sorry. I am silly sometimes.
so because the vertex is (4,8), this means h = 4 and k = 8. I plugged those in
along with a = -2
so you moved -2 to both sides and multiplied 2 and -2?
I got a = -2 from the fact that the slope of each piece of y = |x| is +1 and -1 but the slopes here are +2 and -2, so I doubled things to go from y = |x| to y = 2|x| then I flipped the V over to get y = -2|x|
Ok. Thank you for that clarification. So the function is -2|x-4|+8?
y = -2|x-4|+8 or f(x) = -2|x-4|+8
here's the graph to check https://www.desmos.com/calculator/m8dav9jses
ignore the portions that aren't in quadrant 1
I don't know what to do on there
it's basically a graphing calculator do you see the red V shape graph?
No. It's blank.
I'm sorry. I never used a graphing calculator before.
That's correct, but on my paper the number eight is not labeled.
probably because it's cut off? not sure
Something like that. I need help finding the inverse of the function. The function is not in the regular form to create the inverse of a function.
To find the inverse graphically, you take each point and swap the coordinates eg: (4,8) ---> (8,4) (8,0) ---> (0,8)
I need it in an equation.
later on when you learn about the vertical line test, you'll find that the inverse is NOT a function
I'm sorry, but I'm doing it the way I learned.
have you learned that absolute value functions are made up of two linear equations?
I don't know.
Do you mean like x=2 and x=-2?
so the term "piecewise function" doesn't sound familiar?
No. sorry. I don't know what level math you're in right now.
hmm I'm trying to figure out what the teacher wants and the method s/he wants you to use
He wants me to use composition. Have you ever heard about that?
Ok, I need help with making the function conforming to the composition rules.
I don't need the composition. I think, but it's to check the inverse function.
I'm not sure how he wants you to find the inverse equation if you haven't learned about how an absolute value function is composed of 2 linear equations.
I know what you mean.
all that shows how to find the inverse of a linear equation. So we just need to break up the V shape into 2 linear equations, then find the inverse of each piece
How do I get that?
focus on the left half of the V shape what two points are on this line?
(0,0) and (4,8)
what is the equation of the line through those two points
I don't know. I know the slope.
what's the slope
what's the y intercept?
I think I'm going to be wrong, but is it (2,4)
where does that line cross the y axis?
Ok. I'm feeling silly, but if the line continued wouldn't it be (0,0)
the left line goes through (0,0), yes
slope = 2 ----> m = 2 y intercept = 0 ---> b = 0
the left piece of the line is y = 2x+0 or just y = 2x
The line would just 2x
So the line is 2x without 0?
y=2x+0 is the same as y = 2x it's better to write the most simplified form to make things easier
Ok. I'm going to try and find the inverse.
The y intercept is a zero. It cannot have an inverse.
you need to have an equation like y=x-4/3
It could work.
you can find the inverse of y = 2x though
swap x and y, solve for y
I found it and I made the equation y=2x+0.
you should find the inverse to y = 2x is y = x/2
Ok, because the inverse cannot have zero?
I don't know what you mean by not having 0
Should I use composition?
I think composition is only used to verify you have the correct inverse (as your attached image shows)
I'll use it. I need to make sure they are inverses.
ok so f(x) = 2x and g(x) = x/2 confirm that f( g(x) ) = x and g( f(x) ) = x
I got -2(x/2). Is that correct?
you should have 2(x/2) now simplify that
I got -x and -x for both compositions?
you should get +x
2(x/2) = 2x/2 = x
I'm sorry. I confused myself.
no, f(x) = 2x
I wrote that when I tried it my way.
I fixed it and wrote x and x.
so that confirms x/2 is the inverse of 2x
Yes. I understand that now
now find the equation of the right half of the V
There is no y intercept for the right side. There is a x intercept.
extend the line until it crosses the y axis
or you can use y = mx+b and solve for b
slope = -2 ---> m = -2 point on the line is (8,0) ---> x = 8 and y = 0
y = mx+b y = -2x+b ... replace m with -2 0 = -2*8+b ... replace x with 8, replace y with 0 solve for b
why do you have to replace x with 8?
because we know (8,0) is on that right half of the V
we could use (4,8) as well
Ok. Now I will multiply -2 and 8.
then isolate b
to isolate b I will cross cancel b by adding -b.
why not move the -16 over
0 = -2*8+b 0 = -16+b 16 = b ... Add 16 to both sides. so b = 16 agreed?
I'm starting to forget basic stuff, I'm sorry. I agree.
slope = -2 m = -2 y-intercept = 16 b = 16
y = mx+b turns into y = -2x+16
Ok. I got it. Now I need to find the inverse.
I got the answer. The answer is x and x.
what inverse did you get
The inverse is x and x.
those are the results after you do the composition
what is the actual inverse
I don't know. I'm sorry.
did you solve x = -2y+16 for y?
Yes I did.
and you got y = ??
I got x.
forget about the composition stuff for now
isolate y in `x = -2y+16`
I'm sorry I did not solve it, but if you mean y=x-16/-2
then I did solve it.
you can also write that as y = (16-x)/2
Yes. I'm right. I got the composition correctly right?
yes if you ended up with x for each composition, you confirmed you have the correct inverse
Yes. Can you help with the rest of page? Or are you tired?
how much is left?
three problems and I have the answers I just need to make sure they're right.
ok I can check what you have
Ok. Please wait.
ok, I'll be right back.
for #5 they want you to describe how the parent function is changing
how is y = |x| transformed into that V shape you see?
you agree that the graph of y = |x| looks like this right? |dw:1441247206827:dw|
I don't agree. It's upside down.
well the graph you have is upside down, but that isn't the graph of y = |x|
the two are similar though which is why we apply a bunch of transformations
Mine is not upside down. Mine is right, you're looking at it wrong.
this is what |x| looks like http://demo.activemath.org/ActiveMath2/LeAM_calculusPics/AbsValue.png?lang=en
No it's not, it's going down.
the teacher is trying to get you to transform what I posted into what you have
at some point, the graph will flip
no. It won't we haven't learned that yet.
hmm let me think
it's so strange how they want you to find the inverse when you haven't learned about horizontal/vertical line tests and how they ask about transformations when you haven't covered that either
You're taking harder Algebra.
yeah I'm thinking of a different algebra class maybe
I'm taking Algebra 2. How about you?
your best bet is to ask the teacher since he'll know what he wants
I'm not in algebra, but I'm probably thinking of another algebra class
So your other answers are wrong? There are only two algebra classes.
No I'm quite sure the answers I got are correct. It's just sometimes the teacher wants you to do things a very specific way
Then I am going to cry.