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kirk.freedman
Group Title
The rational function has a yintercept of 7. What is the equation for this function?
 one year ago
 one year ago
kirk.freedman Group Title
The rational function has a yintercept of 7. What is the equation for this function?
 one year ago
 one year ago

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kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
@phi @UnkleRhaukus @robtobey @Mertsj @mathstudent55 @jim_thompson5910 @ghazi
 one year ago

ghazi Group TitleBest ResponseYou've already chosen the best response.1
just shift the origin of hyperbola by (2,5)
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
I'm sorry, I don't really understand.
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
Somebody please please help!
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.1
1) Vertical Asympote @ x = 2 ==> \(\dfrac{Something}{x+2}\) 2) Horizontal Asympote @ y = 5 ==> \(\dfrac{5x  Something}{x+2}\) 3) yintercept (0,7) ==> Something / 2 = 7 ==> \(\dfrac{5x + 14}{x+2}\) 4) Almost. We missed (3,0). How do you suppose we should alter it for that?
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
I'm sorry, I would give it a guess but I really don't know where we would add that
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
what is the (3,0)? is there a name for it like the others?
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.1
xintercept
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
Oh Oh Oh, I am actually understanding this, and I was gonna guess xint, but I thought it was wrong.. So I understand everything, but I just don't know how you can put the xint into the equation :)
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.1
A little more generally... General Form \(\dfrac{axb}{cxd}\) 1) Vertical Asymptote @ x = 2 ==> c(2)  d = 0 ==> d = 2c General Form \(\dfrac{axb}{cx(2c)} = \dfrac{axb}{cx + 2c} = \dfrac{axb}{c(x + 2)}\) 2) Horizontal Asymptote @ y = 5 ==> a = 5c General Form \(\dfrac{5cxb}{c(x + 2)}\) 3) yintercept (0,7) ==> \(\dfrac{b}{2c} = 7\) ==> \(b = 14c\) General Form \(\dfrac{5cx+14c}{c(x + 2)} = \dfrac{c(5x+14)}{c(x + 2)} = \dfrac{5x+14}{x + 2}\). This is very unfortunate. It means we must have the original form wrong onless the last piece just happens to work as desired. 4) xintercept (3,0) ==> \(\dfrac{5(3)+14}{(3) + 2} = \dfrac{15+14}{3+2} = \dfrac{1}{1} = 1\) And we were hoping for zero.
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
Ok, so if it doesn't work out how do I answer it?
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
So would the equation for the function be (5x+14)/(x+2)?
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.1
Nope. Doesn't quite work. It needs some reshaping. \(y = \dfrac{5(x+3)}{x+2}\) hits (3,0) but not (0,7). Very annoying. I have a plan. Let's play like the xintercept is only CLOSE to (3,0). The problem statement didn't actually say that, so maybe it's just an approximate value. In fact, (3,1) looks better than (3,0), so maybe we ARE done! \(y = \dfrac{5x+14}{x+2}\) it is!!!
 one year ago

kirk.freedman Group TitleBest ResponseYou've already chosen the best response.0
Thanks, I appreciate it sooo much! I know how tough it is to type all of this out, but I am sure this will help others too in the future!
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.1
We probably should note the xintercept on which we settled. 5x + 14 = 0 ==> x = 14/5 ==> (14/5, 0). Done. There is actually a little more information in the nature of the vertical asymptote. Maybe we'll run into one of those, later.
 one year ago
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