While doing my homework, I came across a problem asking me to graph a hyperbola with no horizontal or vertical asymptotes, and an oblique asymptote at y= x + 2. Another problem is asking for the graph of a hyperbola with no asymptotes! I am certain this lack of asymptotes is not due to a calculation error on my part, as this is merely a graphing exercise and the worksheet lists the number and variety of asymptote. Any help would be incredibly appreciated as I have no idea how to complete either of the problems (they're listed below for reference).

 

r(x)= x^2 + x - 6 (no horizontal, vertical, or oblique asymptotes)

x - 2

 

r(x)= x^2 - x - 6 (oblique asymptote at y= x + 2, no horizontal or vertical asymptotes)

x - 3

 

Hint : For the first fraction, what is (x²+x-6) divided by (x-2) ?? Can you not simplify it?

Edited April 18, 201312 yr by studiot

Further to studiot - I would think of it as initially factorising (x²+x-6) to (x+..)(x-..) and canceling (same thing and long-winded but factorisation of quadratics is so common). Frankly I think the question is pretty shoddy; if that is the way it is phrased - and the second questions bracket is just wrong