## anonymous one year ago When looking at a rational function f of x equals the quantity x minus six times the quantity x plus three times the quantity x plus four all divided by the quantity x plus six times the quantity x minus three times the quantity x minus four, Jamal and Angie have two different thoughts. Jamal says that the function is defined at x = –6, x = 3, and x = 4. Angie says that the function is undefined at those x values. Who is correct? Justify your reasoning.

1. anonymous

|dw:1438186410074:dw|

2. anonymous

3. welshfella

(x - 6)(x + 3)( x + 4) ----------------- (x + 6)(x - 3)(x - 4)

4. anonymous

Angie is right.

5. welshfella

if x = -6 what do you think the value of the denominator is?

6. welshfella

(-6 + 6)(x - 3)(x - 4) = 0(x + 3)(x - 4)

7. anonymous

Any of the 3 values subbed in will give you a divide by 0 situation.

8. welshfella

9. anonymous

umm kind of

10. welshfella

if we any of the factors are 0 it will make the whole demnominator = 0

11. anonymous

oh ok so then the whole function is zero

12. welshfella

if x = -3 then we have (x + 6) * 0 * (x + 4) = 0

13. anonymous

Anything divide by zero is undefined.

14. welshfella

no only the denominator but dividing by zero doesn't make sense so we say the value of the function is indeterminate

15. welshfella

- or undefined

16. anonymous

oh ok

17. anonymous

Using limit on it doesn't work either cause it diverges.

18. welshfella

5/0 for example does not make any sense - you add an infinite number of zeros together and thay;ll never make 5!!

19. anonymous

it wil still be undefined

20. anonymous

*will

21. welshfella

yep

22. anonymous

As your denominator goes smaller, your answer gets larger and large towards infinity. For example: $\frac{ 1 }{ 0.1 } = 10$ $\frac{ 1 }{ 0.000001 } = 1000000$ You can see the pattern.

23. anonymous

thank you you guys thank you so much i think i might be able to explain it thank you

24. welshfella

yw

25. iseeunicorns

@iwanttogotostanford hope this helps :))

26. seb.cal

@welshfella In your second comment, you wrote x = -6. did you make up that number? Or did you get it from solving anything?

27. seb.cal

@welshfella

28. welshfella

I chose it because it made (x +6) equal to zero