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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
**Posts:**333**Joined:**Mon Mar 30, 2009 1:30 pm**Location:**USA-
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[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

I Cant see your picture/image

- stapel_eliz
**Posts:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
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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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This suggests that the degrees of the numerator and denominator need to be the same.these are the characteristics it has to follow:

lim f(x) = 2 x -> infinty

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

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

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

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

How can you have a max/min point where the function is not defined?relative min of 0 at x=2

Do you really have to get theserelative max of -0.900466 at x=0.442818

concave down (-infinty, -4) (-4,-2) (6.835351, infinty)

concave up (2,6.835351)

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.x-inter (4,0)

So the function is equal to -1 when x = 0.y-inter (0,-1)

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