Limits and continuity?

[petabread]

1) State points where the graph isn't continuous


2.) classify each discontinuity


3.) what vale of x is this equations not differentiable

 

[Deleted member 4993]

1) State points where the graph isn't continuous


2.) classify each discontinuity


3.) what vale of x is this equations not differentiable

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

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[stapel]

Shame on whoever drew that graph! Any instructor worth his salt should know better (as should any beginning algebra student)! Here's my guess as to what the graphic is meant to show:

graph:         ^y
               |      '   
      .O       -      '
    .'         |      '
  .'           |      '
 /           ..-.     '    *
'         .'   | '   '
        .'     |  ' '              ,'
---|---*---|---+---*---|---|---|---> x
               |               ,'
               |             ,'
               -           O'
               |          ,
               |        ,'
               -       O
               |

I have used "O" to designate what I'm assuming are "open" points (being points labelled on the graph for clarity about where a line portion ends, but which are not actually included within that line portion) and "*" to designate other labelled points (being "closed" points which are included in their attached line portions, or are otherwise stand-alone points).

1) State points where the graph isn't continuous

2.) classify each discontinuity

3.) what vale of x is this equations not differentiable

Since the instructions you were given (quoted above) are less well-stated than those in the image, I'll use the better instructions; namely:

. . .1. For which values of x is f (x) not continuous?

. . .2. Classify each discontinuity as left continuous, right continuous, or neither.

. . .3. For which values of x is f (x) not differentiable?

To get started, use what you learned back in algebra about continuous and non-continuous functions. What is the definition of "continuous"? What does it look like, on a graph, when a function is continuous? What does it look like when the function is not continuous? (In particular, think about when you were graphing piecewise functions.)

For part (2), look at your book's definitions of "left continuous" and "right continuous". Which discontinuity fits which definition? Which, if any, fits neither? (By the way, does your book say "neither" includes "both left and right continuous", or not? You'll need to tell us.)

Please reply with your thoughts and efforts on the first two parts. Once you're done with those, we can see about part (3). Thank you!