pre calc
posted by kim on .
find all the horizontal and vertical asymptoes of the functions
f(x)=x/(x1)
q(x)=(x1)/x

When the denominator equals zero, there is a vertical asymptoe
When the numerator becomes constant as x approaches very large, there is a horizontal asymptoe.
For instance, in the second
q(x)=(x1)/x= 11/x as x gets very large, it becomes 10 or 1
In the first,
f(x)=x/(x1)= 1/(11/x) (multiplied numerator and denominator by 1/x)
f(x)= 1/(10) when x is very large, or f(x)=1 
x = 1 for the first one
x = 0 for the second 
yes, for the vertical asy.

so what about this one g(x)=1.5^x

No vertical, no horizontal.

how can you tell it has neither

As Mr. Bob mentioned:
When the denominator becomes zero when x=c and c is finite, there is a vertical asymptote.
A horizontal asymptote is typically identified by the fact that lim f(x) approaches a constant value as x>∞ or > &infin.
In the case of:
g(x)=1.5^x
there is no denominator that makes g(x) infinite when x is finite, so no vertical asymptote.
g(x) becomes infinite when x>+∞, so no horizontal asymptote on the right. But on the left..., as x>∞, g(x) approaches zero, so what do you think?