i have 8(x-2)/(x-4)(x+2) as my answer
help find the equation of this graph
#Help
ionic shale
crystal tundraBOT
leaden seal
,w graph [8(x-2)]/[(x-4)(x+2)] from -10 to 10
old hearthBOT
leaden seal
tis a bit off
ionic shale
i have that answer currently just cant figuire it out
ionic shale
tis a bit off
u stumped?
leaden seal
a bit, im thinking how to modify what you already have to fix it but i got nothing
ionic shale
yeah that what im saying shit just dont make sense
this is the hardest ive ever been in my life
wintry gazelle
You basically need to flip the sign of the graph when x > 4, you do not want any more zeros though so you should add a new factor in the denominator. Since you don't want any more asymptotes either you have to either use x-2, x+2, or x-4 again in the denominator, or multiple of them
ionic shale
You basically need to flip the sign of the graph when x > 4, you do not want any...
wdym
wintry gazelle
wdym
Currently in 8(x-2)/(x-4)(x+2), when x > 4, 8(x-2)/(x-4)(x+2) > 0. Well we want values of our equation to be negative when x > 4, so we should multiply by something that will only change the sign when x > 4 right?
In general when you add things to the numerator of a rational expression, you are changing the behavior of the solutions (when the equation = 0), and when you add things to the denominator, you are changing the behavior of the discontinuities. If you add a copy of a factor though, it does not change the behavior of the solutions/discontinuities, it only changes the behavior of the sign.
For example lets say we add (x-5) to the numerator. This is the new graph we get. We see that the asymptotes stay the same, but we get a new root at x=5
wintry gazelle
Exactly
So if we add anything to the numerator that is not (x-2) we get a new x intercept
ionic shale
correct
wintry gazelle
What happens if we add (x-2)?
We get this graph
It has the same behavior as before (same asymptotes and x-intercepts), but the sign of values if changed
This is not quite what we want though because this doesn't flip the sign of the function ofr x>4, it does stuff around x=2, which is expected since we are multiplying by (x-2)
If we want behavior to change around x = 4, we should multiply by something like (x-4) or 1/(x-4)
This is because for x-4, when x>4, x-4 > 0, and when x<4, x-4 < 0
This is the key to flipping the sign ONLY for values of x > 4
ionic shale
so what woudl the answer be
wintry gazelle
So now you should be thinking we either add (x-4) to the numerator or denominator, but from before we found adding (x-4) to the numerator would create a new x-intercept, which is not what we want, so instead we should consider adding (x-4) to the denominator
Try adding (x-4) to the denominator and the answer will become clear
Your solution will be of the form y = a(x-2)/(x+2)(x-4)(x-4) for some constant a
Since I was trying not to give the entire answer away I gave a lot of information that might not have been clear, but my point was basically you should think about what happens when you add things of the form (x-a) to the numerator and denominator, and see what happens when you do that. Also since we want the behavior to change for x > 4, using a = 4 would be the most obvious choice to experiment with
ionic shale
wintry gazelle
Yup
Now its basically the original image but flipped and scaled
so your gonna need to multiply by a negative constant to flip it vertically, then find the right scale factor
wintry gazelle
Im in my last year of a math undergraduate program
ionic shale
so what math is that
wintry gazelle
Im taking real analysis, abstract algebra, complex analysis, linear algebra, and some other misc courses
chrome plover
I mean I found the answer should I show it?
ionic shale
sure
chrome plover
What do you have currently or is it the same?
chrome plover
