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!
I realise this might be too late for your test, but in any event:
With respect to the first equation, the only asymptotes are x = 0 and y = x^2. y = 2/x is
not an asymptote.
With respect to the second equation the asymptotes are x = 0 and y = x – 5.
In general, to find asymptotes of a rational function, use long division or equating coefficients to express it in the form P(x) + Q(x)/R(x), where P(x) is a polynomial (perhaps of degree 0, ie. just a constant), and where the degree of Q(x) is less than the degree of R(x). When your rational function is in this form, you will have the following asymptotes:
1. P(x) will be an asymptote. This is because as x approaches infinity, Q(x)/R(x) approaches zero. Hence, the only non-vanishing term in the function is P(x).
2. Any values of x for which R(x) = 0 will give a vertical asymptote. This is because the graph is undefined at these values (division by zero), and because Q(x)/R(x) approaches infinity as x approaches these asymptotes.