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j2lie
 one year ago
Does the function represented by the graph have an inverse function? The three coordinates are (0,0), (4,8), and (8,0).
j2lie
 one year ago
Does the function represented by the graph have an inverse function? The three coordinates are (0,0), (4,8), and (8,0).

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2Plot 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.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I cannot, because the line is slanted on the graph.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2did you plot the three points?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0yes. It's been drawn for me.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok is it possible to draw a flat horizontal line through more than one point?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Yes, between zero and eight.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yeah through (0,0) and (8,0) so this means the horizontal line test fails and we won't have an inverse function

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Why? I think there should be an inverse. I just don't know the function for the graph.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2did you learn about the vertical line test?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Not yet. We're talking about functions and graphs. Also domain and range.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2well the rule about functions is that a relation must pass the vertical line test in order to be a function

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2if you can pass a vertical line through more than one point, then the vertical line test fails and we do NOT have a function

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok. But how do I find the function of the graph?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2In this case, we just have 3 points. It seems like there isn't enough information to find the actual function

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2can you post a screenshot of the full thing?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I will check my notes, but they're confusing.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I recommend watching this video about the vertical line test https://www.youtube.com/watch?v=xvDn4FOJQ hopefully it will help

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I haven't learned that yet, so would it count if put the vertical and horizontal tests as my answer?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2if 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)

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I 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.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2can you post a screenshot of the full thing?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I cannot attach a picture.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the "attach file" button isn't working?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2maybe host it on a site like imgur and then paste the link

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2that might work, just as long as you can host the image somewhere and share the link

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0My username is princess5062. You can see the picture that I just uploaded.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0https://instagram.com/p/7Ja6_CmGRgNTAiNKsvvsYhyWXzo4VLMRi9m1A0/?takenby=princess5062

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2it's telling me "Sorry, this page isn't available"

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0you have to have an account. It worked when I was logged on.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2oh sorry I don't have an account. There's no way to share to nonaccount holders?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0maybe I should i create an imgur account

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you don't need to create one, they allow you to upload without an account

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok so it's a V shaped line, I see now

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0That's what I said like a parabola.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok 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.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Oh. 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?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2no, 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2`Can I use any information I wrote down for the function?` I'm not sure what you mean

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Like the average rate of change, can I put that in an equation that is the function of the graph?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2oh, yes you can to describe the slope of each piece of the V shape

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so for #3, you'll have 2 answers there

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0That's the average rate of change also known as slope.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I got 2 and 2 for the rate of change. There is an inverse, because the signs are the opposite.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes for the first half from 0 to 4, the slope is +2 the second half from 4 to 8 has the slope 2

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Is it going to be an equation or inequality?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the graph you mean?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Yes, the function of the graph.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the function is an equation

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I thought it was an equality, because 2 and 2 are opposite of each other.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0so the equation is y=x + 2 = 2?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2equality is the same as equation both have "equa" in them an inequality is something like y > 2x which would involve shading

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the 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 = axh+k y = 2x4 + 8 is your equation

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0The function is not an equation with the letter y. We have to find the equation for the function.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you can replace y with f(x)

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I might be wrong, because I looked at problem six, it's asking for an equation of the function.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yeah you start with y = x and do a bunch of transformations to end up with y = 2x4 + 8

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Where did you get the eight?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2that's the y coordinate of the vertex

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1441239501121:dw

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Thank you. How did you get the equation? Sorry, I'm not understanding your equation.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I started with the template y = axh+k

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2have you learned about y = axh+k ?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Did you multiply 2 and 2?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I haven't learned that yet.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I did, I'm so sorry. I am silly sometimes.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so because the vertex is (4,8), this means h = 4 and k = 8. I plugged those in

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2along with a = 2

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0so you moved 2 to both sides and multiplied 2 and 2?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I 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 = 2x then I flipped the V over to get y = 2x

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok. Thank you for that clarification. So the function is 2x4+8?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2y = 2x4+8 or f(x) = 2x4+8

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2here's the graph to check https://www.desmos.com/calculator/m8dav9jses

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ignore the portions that aren't in quadrant 1

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I don't know what to do on there

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2it's basically a graphing calculator do you see the red V shape graph?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you should see this

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry. I never used a graphing calculator before.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0That's correct, but on my paper the number eight is not labeled.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2probably because it's cut off? not sure

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Something 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.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2To find the inverse graphically, you take each point and swap the coordinates eg: (4,8) > (8,4) (8,0) > (0,8)

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I need it in an equation.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2later on when you learn about the vertical line test, you'll find that the inverse is NOT a function

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry, but I'm doing it the way I learned.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2have you learned that absolute value functions are made up of two linear equations?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Do you mean like x=2 and x=2?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so the term "piecewise function" doesn't sound familiar?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0No. sorry. I don't know what level math you're in right now.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2hmm I'm trying to figure out what the teacher wants and the method s/he wants you to use

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0He wants me to use composition. Have you ever heard about that?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok, I need help with making the function conforming to the composition rules.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I don't need the composition. I think, but it's to check the inverse function.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I'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.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2all 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2focus on the left half of the V shape what two points are on this line?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what is the equation of the line through those two points

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I don't know. I know the slope.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what's the slope

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what's the y intercept?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I think I'm going to be wrong, but is it (2,4)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2where does that line cross the y axis?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok. I'm feeling silly, but if the line continued wouldn't it be (0,0)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the left line goes through (0,0), yes

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2slope = 2 > m = 2 y intercept = 0 > b = 0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the left piece of the line is y = 2x+0 or just y = 2x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1441241810907:dw

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0So the line is 2x without 0?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2y=2x+0 is the same as y = 2x it's better to write the most simplified form to make things easier

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok. I'm going to try and find the inverse.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0The y intercept is a zero. It cannot have an inverse.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0you need to have an equation like y=x4/3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you can find the inverse of y = 2x though

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2swap x and y, solve for y

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I found it and I made the equation y=2x+0.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you should find the inverse to y = 2x is y = x/2

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok, because the inverse cannot have zero?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I don't know what you mean by not having 0

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Should I use composition?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I think composition is only used to verify you have the correct inverse (as your attached image shows)

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'll use it. I need to make sure they are inverses.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok so f(x) = 2x and g(x) = x/2 confirm that f( g(x) ) = x and g( f(x) ) = x

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I got 2(x/2). Is that correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you should have 2(x/2) now simplify that

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I got x and x for both compositions?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you should get +x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.22(x/2) = 2x/2 = x

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry. I confused myself.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2no, f(x) = 2x

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I wrote that when I tried it my way.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I fixed it and wrote x and x.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so that confirms x/2 is the inverse of 2x

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Yes. I understand that now

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2now find the equation of the right half of the V

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0There is no y intercept for the right side. There is a x intercept.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2extend the line until it crosses the y axis

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2or you can use y = mx+b and solve for b

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2slope = 2 > m = 2 point on the line is (8,0) > x = 8 and y = 0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2y = mx+b y = 2x+b ... replace m with 2 0 = 2*8+b ... replace x with 8, replace y with 0 solve for b

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0why do you have to replace x with 8?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2because we know (8,0) is on that right half of the V

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2we could use (4,8) as well

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok. Now I will multiply 2 and 8.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2then isolate b

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0to isolate b I will cross cancel b by adding b.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2why not move the 16 over

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.20 = 2*8+b 0 = 16+b 16 = b ... Add 16 to both sides. so b = 16 agreed?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'm starting to forget basic stuff, I'm sorry. I agree.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2slope = 2 m = 2 yintercept = 16 b = 16

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2y = mx+b turns into y = 2x+16

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1441243656946:dw

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Ok. I got it. Now I need to find the inverse.

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I got the answer. The answer is x and x.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what inverse did you get

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2those are the results after you do the composition

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what is the actual inverse

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I don't know. I'm sorry.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2did you solve x = 2y+16 for y?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2and you got y = ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2forget about the composition stuff for now

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2isolate y in `x = 2y+16`

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry I did not solve it, but if you mean y=x16/2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you can also write that as y = (16x)/2

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Yes. I'm right. I got the composition correctly right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes if you ended up with x for each composition, you confirmed you have the correct inverse

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Yes. Can you help with the rest of page? Or are you tired?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2how much is left?

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0three problems and I have the answers I just need to make sure they're right.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok I can check what you have

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok, I'll be right back.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2for #5 they want you to describe how the parent function is changing

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2how is y = x transformed into that V shape you see?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you agree that the graph of y = x looks like this right? dw:1441247206827:dw

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I don't agree. It's upside down.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2well the graph you have is upside down, but that isn't the graph of y = x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the two are similar though which is why we apply a bunch of transformations

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0Mine is not upside down. Mine is right, you're looking at it wrong.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2this is what x looks like http://demo.activemath.org/ActiveMath2/LeAM_calculusPics/AbsValue.png?lang=en

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0No it's not, it's going down.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the teacher is trying to get you to transform what I posted into what you have

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2at some point, the graph will flip

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0no. It won't we haven't learned that yet.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2hmm let me think

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2it'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

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0You're taking harder Algebra.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yeah I'm thinking of a different algebra class maybe

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0I'm taking Algebra 2. How about you?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2your best bet is to ask the teacher since he'll know what he wants

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I'm not in algebra, but I'm probably thinking of another algebra class

j2lie
 one year ago
Best ResponseYou've already chosen the best response.0So your other answers are wrong? There are only two algebra classes.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2No 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
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.