## math456 3 years ago Need help! Explain why the function is discontinuous at the given number a. Sketch the graph of the function!

1. math456

2. math456

@cwrw238 @Hero

3. math456

@jim_thompson5910

4. jim_thompson5910

what is cos(0)

5. math456

its 1

6. jim_thompson5910

so notice how in the first piece, the y value at x = 0 is 1 but the y value in the second piece at x = 0 is 0 Can you visualize what I'm describing?

7. math456

yea so that means $\cos x \neq x=0$

8. jim_thompson5910

do you mean cos(x) doesn't equal x when x = 0?

9. math456

yea because at x its 0 and at x<0 its 1

10. jim_thompson5910

then you are correct, and this shows us that there is a discontinuity

11. math456

alright kool thanks and does the graph looks like this?|dw:1348180882506:dw|

12. jim_thompson5910

you're on the right track

13. jim_thompson5910

however, you only graph cos(x) when x < 0

14. jim_thompson5910

and you only graph 1 - x^2 when x > 0

15. jim_thompson5910

make sure you draw a hole at (0,1) and a closed circle at (0,0)

16. math456

|dw:1348181069990:dw| like this?

17. jim_thompson5910

closer, but now erase the piece of cos(x) that's to the right of x = 0 and erase the piece of 1 - x^2 that's to the left of x = 0

18. math456

|dw:1348181225073:dw|

19. jim_thompson5910

good, you got it

20. math456

alright thanks for ur help!

21. jim_thompson5910

np