Okay first note that you can actually write this asHello again, this time I am trying to plot and trying to find the equations of all asymptotes. I found that there's no vertical asymptotes. But I am not sure how to find horizontal asymptote. Do I just manually sub in values? It is too much work by hand... Is there any simpler way? Thanks in advance.
Note that there is an asymptote at x=0.
From there differentiate to find that
Note that this curve has no real stationary points, and also by noting that
that the function is monotonic increasing.
Noting from before that x=0, find the limiting behaviour of the curve as it approaches 0 from both sides, and positive and negative infinity.
You should find that it approaches y=x from beneath on the positive side, and from above on the negative side as it approaches positive and negative infinity respectively. SImilarly, as it approaches zero from the positive side, you get that it tends to negative infinity, while from the negative side it tends to positive infinity. You should get a graph like this (red is the function, blue is y=x (just to show that it is also an asymptote))Spoiler(https://i.imgur.com/ylTZrni.jpg)
Hope this helps :)
Hello again, this time I am trying to plot and trying to find the equations of all asymptotes. I found that there's no vertical asymptotes. But I am not sure how to find horizontal asymptote. Do I just manually sub in values? It is too much work by hand... Is there any simpler way? Thanks in advance.
SnipHey, I didn't do spec & have never been assessed on this so take what a say with a grain of salt. But:
Hello I have a test today on this topic and I am still not sure about graphing. Some questions like has and as the asymptote. But not all questions have both things as the asymptote. For example, only has as its asymptote and not . Is there any particular rule for this? Really urgent I have a test today on period 5. Thanks to anyone who answers my question!