## anonymous 3 years ago Can someone please help me I am stuck... How do the graphs of y=1/x and y=5/x+6 compare?

1. stamp

$y_{1}=\frac{1}{x},\ y_{2}=\frac{5}{x+6}$Can you visualize y1 or y2? If so, draw a sketch of the graph(s)

2. stamp

It might help to think of y2 as$y_{2}=5(\frac{1}{x+6})$

3. anonymous

What happened to the other x?|dw:1360212091432:dw|

4. anonymous

Thats what my graph is suppose to look like, but I need to know how they compare.

5. blurbendy

is the second one y = (5/x) +6 or y = (5) / (x+6) ?

6. anonymous

The second one

7. anonymous

|dw:1360212481953:dw|

8. blurbendy

I think you have the graphs for y = 1/x and y = (5/x) +6 not (5) / (x +6)

9. anonymous

|dw:1360212546332:dw|

10. anonymous

|dw:1360212588584:dw|

11. anonymous

It does not say on my graph

12. anonymous

|dw:1360212632344:dw|

13. anonymous

^Thats the right graph but how do they compare

14. anonymous

i showed points on both the graphs when the +6 term comes the graph is moved to the left 6 steps

15. anonymous

|dw:1360213092724:dw|

16. anonymous

Oh okay

17. anonymous

Well it still doesnt make sense

18. anonymous

it does both are same things but the one graph is a little wide near the origin and u get y=5 for x=1

19. anonymous

and then it is moved to the left

20. anonymous

both are hyperbolas but only thats the difference

21. anonymous

well I need an equation

22. anonymous

u see the magniture of the function increased with multiplying by 5 and graph shifted to the left with the 6

23. anonymous

magnitude

24. agent0smith

For an equation to compare them... lets call them f1(x) and f2(x) $f _{1}(x) = y _{1} =\frac{ 1 }{ x }$$f_{2}(x) = y _{2} =\frac{ 5 }{ x+6 } = 5\left( \frac{ 1 }{ x+6 } \right)$

25. agent0smith

$f _{2}(x) =5 \times f _{1}(x+6)$