## sakigirl 2 years ago How do you find the domain and range of y=(1/x)-5?

1. sakigirl

2. sakigirl

|dw:1359707995799:dw|

3. dpaInc

notice the vertical asymptote... at x = ??? this should give you a hint for the domain... notice the horizontal asymptote... at y = ??? this should give you a hint for the range.

4. skullpatrol

What happens at x = 0?

5. jim_thompson5910

Hint: To find the domain, find all the values of x that make the denominator equal to zero To find the range, find the inverse function and repeat the same steps to find the domain

6. sakigirl

I'm confused with this one because there are two lines. It throws me off. Should I put them together or what?

7. skullpatrol

What do the "lines" mean?

8. sakigirl

I'm not really sure what they mean, they're just lines

9. sakigirl

The two curve lines

10. skullpatrol

|dw:1359708410347:dw|

11. skullpatrol

What is the domain and range of this equation?

12. sakigirl

This is what I'm having trouble with. I don't know how to find the domain and the range for these kinds of functions

13. skullpatrol

The domain is all the values that you are allowed to input into the equation.

14. jim_thompson5910

ignore the graph look at the equation y = (1/x) - 5 x cannot be 0 because if it were, then you would be dividing by zero (which is not allowed) so you must restrict 0 from the domain any other number is just fine So the domain is the set of all real numbers but x cannot be zero

15. jim_thompson5910

the range can be found in a similar way, but you first need to find the inverse function

16. skullpatrol

What would those be for $$y=\frac{1}{x}$$

17. sakigirl

What do you do after you find the inverse function?

18. jim_thompson5910

what did you get for the inverse function

19. sakigirl

Actually, nevermind.

20. sakigirl

I want to be able to look at the graph and know the domain and the range

21. jim_thompson5910

I'll show you how to get the inverse function Swap x and y, then solve for y y = (1/x) - 5 x = (1/y) - 5 x+5 = 1/y y(x+5) = 1 y = 1/(x+5) So the inverse function is y = 1/(x+5)

22. jim_thompson5910

what makes the denominator x+5 equal to zero ?

23. jim_thompson5910

we can go back to the graph after we do these equations

24. sakigirl

Wait, hold on. @skullpatrol is it |dw:1359709153164:dw|

25. skullpatrol

Yes, and why?

26. skullpatrol

|dw:1359709317420:dw|

27. skullpatrol

|dw:1359709670237:dw|

28. skullpatrol

Compare your graph to mine :)

29. sakigirl

That's what I got

30. sakigirl

x=/=0 y=/=-5