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
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.
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.