## anonymous one year ago Graph 3/x^2-4. Then find the domain/range/VA

1. Astrophysics

$f(x) = \frac{ 3 }{ x^2 }-4?$ is this your equation, think of the parent function, which in this case is $\frac{ 1 }{ x^2 }$ it looks like |dw:1439265308847:dw| you can get this by simply making a table of values which you can do yourself. Once you have your parent function now we can do our transformations. $y = \frac{ 3 }{ x^2 }$ where the 3 should give you a scaling factor then afterwards add the -4, $y = \frac{ 3 }{ x^2 }-4$ where the -4 should give you a vertical translation of -4 units. If you're not comfortable at seeing it directly you can always make a table of values for each step, good luck!

2. anonymous

No:( It is |dw:1439336098501:dw|

3. anonymous

I'm sorry lol:)

4. Astrophysics

That means you're graph will look like this then |dw:1439336233138:dw|

5. Astrophysics

Actually here, use this site to graph it out, but make sure you know how the transformations work https://www.desmos.com/calculator

6. anonymous

Thanks:)! What about the domain, range

7. Astrophysics

For domain solve $x^2 - 4 \neq 0$ solve for x

8. anonymous

um -2 or 2?

9. Astrophysics

Yup, exactly

10. Astrophysics

Notice that domain occupies the x values, and range is the y values so you have y>0 and $y \le -3/4$

11. anonymous

ok:) And what about the VA? I have no idea what that means haha

12. Astrophysics

vertical asymptotes

13. Astrophysics

I'm assuming you don't know what limits are, so you see where it's not defined

14. Astrophysics

So VA is at x = 2 and x = -2

15. anonymous

And last one, I promise :) It says find the HA/SA???

16. Astrophysics

I don't know what SA is but HA is horizontal asymptote

17. anonymous

Okay so would that be -3/2?

18. Astrophysics

Not quite, since the denominator has a higher degree than the numerator it's 0

19. Astrophysics

That's just a shortcut though

20. Astrophysics

You should actually look up what exactly this stuff means haha

21. anonymous

lol! I probably should :) and I will

22. anonymous

so just checking, so far we have: VA=-2,2 D-all real numbers r-y<=-3/4

23. Astrophysics

domain is not all real numbers

24. Astrophysics

X cannot be -2 and 2

25. anonymous

oh.

26. Astrophysics

$D: x \in \mathbb{R}: x \neq \pm 2$

27. Astrophysics

It's all real except for + and - 2

28. anonymous

ok:) Thanks :)

29. Astrophysics

$R: y \in \mathbb{R}: y \le - \frac{ 3 }{ 4 } ~or~y>0$

30. anonymous

So going back to the horizontal asym., I sort of get it know : http://www.purplemath.com/modules/asymtote2.htm

31. anonymous

Thanks:)

32. anonymous

so it would be 3/x^2?

33. Astrophysics

y=0

34. anonymous

Thanks so much:)))

35. Astrophysics

and if the degree in the numerator was greater you'd have no horizontal asymptote, so like (x^3+2)/(x^2+3) no HA