## help creating rational function impossible

Limits, differentiation, related rates, integration, trig integrals, etc.
jbirdwell
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Joined: Sat Nov 06, 2010 3:26 pm
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### help creating rational function impossible

these are the characteristics it has to follow:
lim f(x) = 2 x -> infinty

lim f(x) = -2 x-> - infinty

lim f(x) = - infinty x-> -4

lim f(x) = - infinty x-> 2-

lim f(x) = infinty x-> 2+

relative min of 0 at x=2
relative max of -0.900466 at x=0.442818
concave down (-infinty, -4) (-4,-2) (6.835351, infinty)
concave up (2,6.835351)
x-inter (4,0)
y-inter (0,-1)
vertical asymptotes at x=2, x=4
Last edited by jbirdwell on Sat Nov 06, 2010 4:18 pm, edited 2 times in total.

Martingale
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### Re: help creating rational function impossible

[img]H:\Photo0217.jpg[/img]

these are the characteristics it has to follow:

lim f(x) = 2 lim f(x) = -2 lim f(x) = - infinty lim f(x) = - infinty lim f(x) = infinty
x -> infinty x-> - infinty x-> -4 x-> 2- x-> 2+

relative min of 0 at x=2
relative max of -0.900466 at x=0.442818
concave down (-infinty, -4) (-4,-2) (6.835351, infinty)
concave up (2,6.835351)
x-inter (4,0)
y-inter (0,-1)
vertical asymptotes at x=2, x=4

Hi jbirdwell,

stapel_eliz
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Are you supposed to come up with "the" function, or just "a" function, that fits the listed criteria?

jbirdwell
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Joined: Sat Nov 06, 2010 3:26 pm
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### Re: help creating rational function impossible

come up with a function that fits all of the characterics

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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these are the characteristics it has to follow:
lim f(x) = 2 x -> infinty
lim f(x) = -2 x-> - infinty
This suggests that the degrees of the numerator and denominator need to be the same.
lim f(x) = - infinty x-> -4
This says that there is a vertical asymptote at x = -4, so there is a factor of x + 4 in the denominator. Also, the sign on f(x) will not change as x passes -4. (Hint: What would happen to the sign of, say, (x + 4)2?)
lim f(x) = - infinty x-> 2-
lim f(x) = infinty x-> 2+
This says that there is a vertical asymptote at x = 2, so there is a factor of x - 2 in the denominator. Also, the sign on f(x) will change as x passes 2.
relative min of 0 at x=2
How can you have a max/min point where the function is not defined?
relative max of -0.900466 at x=0.442818
concave down (-infinty, -4) (-4,-2) (6.835351, infinty)
concave up (2,6.835351)
Do you really have to get these exact values???
x-inter (4,0)
So the function is equal to zero at x = 4, so the numerator is zero at x = 4, so there is a factor of x - 4 in the numerator.
y-inter (0,-1)
So the function is equal to -1 when x = 0.

You should be able to at least get started with the above. Please reply with your thoughts and work so far.