Critical numbers question

Question

function: h(x)=x+2/x-2

If I have a function like this where there ends up being no critical numbers, to determine where the function is increasing or decreasing do I just use the domain of the original function and plug in numbers into the derivative to figure out whether its increasing or decreasing.

Answer 1

y= (x+2)/(x-2)

plot a few points

the graph shows it's everywhere decreasing

except at x=2 where the function is undefined.

x, y

-3, 1/5

-2, 0

-1, -1/3

0 -1

1 -3

2 undefined

3 5

4 3

asymptotes are

vertically x=2

and horizontally y=1

y decreases everywhere

except at x =2 where y jumps from -infinity to +infinity, a big increase, as big as it gets