continuity

[thepie]

Find the x values (if any) at which f is not continuous. Is this discontinuity removable?

f(x)= Ix-3I/x-3

 

[Deleted member 4993]

Find the x values (if any) at which f is not continuous. Is this discontinuity removable?

f(x)= Ix-3I/x-3

Investigate the behaviour of the function as you approach x = 3 - from the left and from the right. Use your graphing calculator.

Please share with us your work/thoughts, indicating exactly where you are stuck - so that we know where to begin to help you

 

[thepie]

I'm not suppose to use my calculator, and I'm not sure how to start the problem.

 

[Deleted member 4993]

I'm not suppose to use my calculator, and I'm not sure how to start the problem.

Then plot it by hand - that's not too difficult...

 

[BigGlenntheHeavy]

$\displaystyle f(x) \ = \ \frac{|x-3|}{x-3}.$

$\displaystyle If \ x \ is \ greater \ than \ three, \ then \ f(x) \ = \ 1.$

$\displaystyle If \ x \ is \ less \ than \ three, \ then \ f(x) \ = \ -1.$

$\displaystyle If \ x \ = \ three, \ then \ f(x) \ is \ undefined; \ the \ discontinuity \ is \ nonremovable.$