# Thread: Using the graph sketching strategy

1. ## Using the graph sketching strategy

Hi all
I wasn't sure which forum to post this in but it does contain calculus so I hope it's in the right place.
I have to use the graph sketching strategy to sketch the graph of the function
(6x-5)/(4-9x^2)

I know this is a long process and I've been doing similar ones with no problems but for some reason I can't seem to make this one work. Any help would be so great!

2. ## Re: Using the graph sketching strategy

By the graph sketching strategy you mean finding minima, maxima, and asymptotes?

If you're having trouble getting started, try finding the two vertical asymptotes.

- Hollywood

3. ## Re: Using the graph sketching strategy

I've so far got that the 2 vertical asymptotes are x=2/3 and x=-2/3.
I also think that 4/3 and 1/3 are stationary points on the graph, although would you mind checking this as I'm not sure I differentiated it correctly?
Many thanks.

4. ## Re: Using the graph sketching strategy

That's correct. Since there are two vertical asymptotes, there will be three "pieces" to the graph. For x < -2/3, the numerator and denominator are both negative, so the function is positive, and it has small values at the left. It goes to positive infinity as it approaches the asymptote. Can you do the other two pieces?

You can check your answer here: plot (6x-5)/(4-9x^2), -2<x<2, -2<y<2 - Wolfram|Alpha

No peeking!

- Hollywood