ƒ(x)= (3x-2)/(x+7)
1) Use interval notation to indicate where f(x) is increasing, and decreasing

Question

ƒ(x)= (3x-2)/(x+7)
1) Use interval notation to indicate where f(x) is increasing, and decreasing

anonymous · Answer

Want to use algebra or calculus on this?

anonymous · Answer

thats an awesome question.. powerful.

anonymous · Answer

You can use standard algebra techniques for rational functions to find the horizontal and vertical asymptotes, then plot a few points on a graph to see what it's doing.
Or you can use the first and second derivative tests from calculus to find the regions of increase/decrease.

anonymous · Answer

thanks, i'm using the calc, i figure out the answer its 
 (-inf,-7) U (-7,inf ) for increasing and an empty {} for decreasing 

Now i'm looking for the horizontal and vertical asymptotes

anonymous · Answer

You can tell from your intervals where the vertical one is.

anonymous · Answer

The horizontal you can find by taking the limits as the function goes to -∞ and +∞.

anonymous · Answer

did you take the derivative? that is the first step

anonymous · Answer

using the quotient rule, you should get 
$$f'(x)=\frac{28}{(x+7)^2}$$ which is clearly positive for all values of $x$ except of course at $x=-7$ where it is undefined. 

your original function is undefined there as well, so your function is increasing on its entire domain, which is all numbers except $-7$

anonymous · Answer

thanks much all! really appreciate !

anonymous · Answer

good to be back again, meeting up with some of you guys, i mean your names are pretty familiar!