## Study23 3 years ago Range on this function!!!!!

1. Study23

|dw:1347947263239:dw|

2. mukushla

this one is a little bit hard to get...at least for me but i'll do it with $x=\frac{2}{\cos \theta}$with $$0<\theta<\pi$$

3. mukushla

because i know domain is |x|>2

4. experimentX

is it -2 to inf?

5. experimentX

looks like there a hole.

6. mukushla

it becomes$y=4\frac{\frac{1}{\cos \theta}+1}{|\tan \theta|}$

7. Study23

$$\ cos \theta?$$

8. mukushla

range is$(-2,0)\cup (2,\infty)$

9. mukushla

yeah $$\cos \theta$$ do u know why ?

10. Study23

No, I don't

11. experimentX

oh ... i didn't realize $\frac{2 ( \sqrt{x+ 2})^2}{\sqrt{x+2}\sqrt{x-2}}= \frac{2 \sqrt{x+2}}{\sqrt{x-2}}$ there isn't asymptotic behaviour at x=-2

12. Study23

? I don't get the whole cos thing... and where did the 2 come from?

13. mukushla

wait forgot cos thing...

14. mukushla

exper got it

15. experimentX

check for these behaviour on these intervals (-inf, -2), (-2, 2), (2, inf)

16. Study23

? How?

17. experimentX

the - infinity part is always confusing, don't cancel .... for that. rest is just same as you did.

18. experimentX

the - infinity part is always confusing, don't cancel to for that. rest is just same as you did.