Hi guys,
So when it comes to finding horizontal/vertical asymptotes for hyperbolas, we have to show full working out despite the fact there are shortcuts with limits etc.
The thing is, we haven't done limits yet in 2U (at my school) so we're not expected to use it in the exam. Instead, we have to "split" the hyperbolic function.
E.g. Given the function f(x) = x/x-1, find asymptotes.
To split, we basically split the "x" up so it becomes
f(x) = (x-1+1)/(x-1), and then,
f(x) = (x-1)/(x-1) + 1/(x-1)
f(x) = 1 + 1/(x-1)
So then we look at the constant "1" and say that's the horizontal asymptote. Let x-1 = 0, then x = 1 is vert. asympt.
But if we're given a complicated hyperbola with both linear expressions on numerator and denominator:
e.g. f(x) = (2x+1)/(5-2x) or f(x) = (-7x+1)(x-6) or f(x) = (-1 + 5x)/(5-7x)
then how are we supposed to "split" it?
I'm really confused atm. Usually I just "look" at the leading co-efficients then I get the HA straight away. Likewise, all I do is let denominator = 0 to find VA.
Have an upcoming 2U exam. Some please come to my aid!
Thanks.
So when it comes to finding horizontal/vertical asymptotes for hyperbolas, we have to show full working out despite the fact there are shortcuts with limits etc.
The thing is, we haven't done limits yet in 2U (at my school) so we're not expected to use it in the exam. Instead, we have to "split" the hyperbolic function.
E.g. Given the function f(x) = x/x-1, find asymptotes.
To split, we basically split the "x" up so it becomes
f(x) = (x-1+1)/(x-1), and then,
f(x) = (x-1)/(x-1) + 1/(x-1)
f(x) = 1 + 1/(x-1)
So then we look at the constant "1" and say that's the horizontal asymptote. Let x-1 = 0, then x = 1 is vert. asympt.
But if we're given a complicated hyperbola with both linear expressions on numerator and denominator:
e.g. f(x) = (2x+1)/(5-2x) or f(x) = (-7x+1)(x-6) or f(x) = (-1 + 5x)/(5-7x)
then how are we supposed to "split" it?
I'm really confused atm. Usually I just "look" at the leading co-efficients then I get the HA straight away. Likewise, all I do is let denominator = 0 to find VA.
Have an upcoming 2U exam. Some please come to my aid!
Thanks.