## anonymous one year ago Use graphs and tables to find the limit and identify any vertical asymptotes of the function

1. anonymous

2. freckles

well the graph of f(x)=1/x is very similar |dw:1433571747343:dw|

3. freckles

|dw:1433571768376:dw|

4. anonymous

I plugged it into my calculator and got the table

5. freckles

notice g(x)=1/(x-10) is just going to have the va moved over to the right 10 units

6. freckles

since x-10=0 gives us x=10

7. freckles

|dw:1433571829590:dw|

8. freckles

|dw:1433571854644:dw| do you see the invisible vertical line that the function is getting closer to find the right and left?

9. freckles

from* (not find)

10. anonymous

Yes that is the asymptote?

11. freckles

yes

12. freckles

and don't forget 10 is not an equation you would need to write x=10 this is the vertical line that I drew in the above picture

13. anonymous

Okay!

14. freckles

now it looks like your question asks us to find the limit since plugin in 10 gives 1/0 we know we have either -inf or inf and we definitely know we have a va at x=10 since we get something/0 where the something isn't 0 when pluggin in 10

15. freckles

to determine if we have -inf or inf look at the y values

16. freckles

determine if they are negative or positive to the left of x=10

17. anonymous

negative, getting smaller

18. freckles

|dw:1433572044573:dw| these points are getting lower and lower

19. freckles

yes

20. freckles

well they actually call it negative large or negative infinity

21. anonymous

ok, is there anything else i need to answer this question?

22. freckles

if wanted the right limit that would look like this in pretty math symbols $\lim_{x \rightarrow 1^+}\frac{1}{x-10}$ |dw:1433572155988:dw| so from the right you would say the y's approach positive infinity or just infinity anyways answer to your question is do you do a table because it ask for a table too not just a graph

23. freckles

|dw:1433572247181:dw| chose some values of x and found out what the corresponding y value is like you can probably use the one's in the table or maybe use x=5 x=9 x=9.05 x=9.99 x=9.99 you are just trying to figure out what is happening to 1/(x-10) for those x's