Continuity of a function

[Guest]

I'm not too sure how to do this question, I think that may be some subtracting involved possibly?Well, here's the question,

Examine the continuity of the function f(x)= x, if x is less than or greater than 1.
1, if 1<x and is less to and equal to 2.
3, if x>2.

Thanks for the help ahead of time


ps. how do you use all the fancy stuff on this thing? ie. equal and less than signs

 

[soroban]

Hello, bittersweet!

Did you make a sketch?

Examine the continuity of the function: \(\displaystyle \:f(x)\;=\,\left{\begin{array}{ccc}\;x\;\;\;x\,\leq\,1 \\ \;\;\;1 \;\;1\,<\,x\,\leq\,2 \\ 3\;\;x\,>\,2\end{array}\)

Can you read it?

For \(\displaystyle x\,\leq\,1\), the graph is the slanted line: \(\displaystyle y\,=\,x\)

For \(\displaystyle 1\,<\,x\,<\,2\), the graph is the horizontal line: \(\displaystyle y\,=\,1\)

For \(\displaystyle x\,<\,2\), the graph is the horizontal line: \(\displaystyle y\,=\,2\)

            |
           2+       o****
            |
           1+   *****
            | *
      ------*---+---+--------
          * |   1   2
        *   |

Now can you discuss its continuity?