sketch graph

[mathgeek]

How would I sketch this graph.

f(x)=(x+1)/(x-1)

I know that the vertical asymptote is (x=1)
I know that the horizontal asymptote is (y=1)

I also know that the first derivative is (-2)/(x-1)^2
I also know that the second derivative is (4)/(x-1)^3

What other information can I find???? :?

 

[galactus]

How would you graph it?. A graphing calculator. Graphing by hand these days is as anachronistic as a slide rule.

Yes, the VA is at x=1 and the HA is at y=1.

That's about it.

The nth derivative is \(\displaystyle \frac{d^{n}x}{dx^{n}}=\frac{(-1)^{n}\cdot 2\cdot n!}{(x-1)^{n+1}}\)

You could throw that in to show off a wee bit

 

[mathgeek]

So this one would be hard to do??? I was just looking in the review section for my calc section and came across this one. I got the vertical asymptotes and the x and y intercept and then I graphed it just on intuition, and got it right.
I was just wondering if this would be very complicated with only about 4 weeks of calculus under my belt.

 

[mmm4444bot]

I was just wondering if this would be very complicated with only about 4 weeks of calculus under my belt.

Have you graphed anything like this before calculus? I'm thinking that Rational functions and their graphs are pre-calculus topics. :?

 

[galactus]

As mmm said, this is not complicated. More like a pre-calc problem.

Rational functions can be differentiated using the quotient or product rules. Asymptotes are more like pre-calc and college algebra material.