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原帖由 lead113 於 2014-4-3 11:06 PM 發表
thnx, graph is like this, dse 未必會考, depends on the level of difficulties in 2014 dse, add oil
This question can be attempted without knowing the exact shape of the function.
However, you need to be familiar with the behaviour of elementary functions at the 2 ends.
The easiest asymptote to determine is normally the vertical asymptote.
There is no denominator or "hidden denominator" here. => no vertical asymptote
Examples of "hidden denominator":
tan x, which is actually sin x/cos x
sec x, which is actually 1/cos x
Now, check oblique asymptote (including horizontal) at the 2 ends.
On the +inf side, the function is dominated by e^x, which grows exponentially. => no oblique asymptote
On the -inf side, e^x -> 0 and arctan x -> -pi/2. There is an asymptote y=0-1+4(-pi/2)=2pi-1
Generally speaking, if f(x) -> ax+b and g(x) -> cx+d, then p f(x) + q g(x) -> p(ax+b)+q(cx+d).