Below is an "oracle" function. An oracle function is a function presented interactively. When you type in an $x$ value, and press the $--$f$-->$ button and the value $f(x)$ appears in the right hand window. There are three lines, so you can easily calculate three different values of the function at one time.

To be safe, keep your $x$ values limited to $10$ decimal places.

Determine the limits for the function $f$ at $3\mathrm{.}53.$

$\underset{x{3\mathrm{.}53}^{-}}{lim}f(x)=$

$f(3\mathrm{.}53)=$

$\underset{x{3\mathrm{.}53}^{+}}{lim}f(x)=$

Are all of these values the same?: $(Y$ or $N)$ If so then the function is continuous at $3\mathrm{.}53$

Are the left and right limits the same at $3\mathrm{.}53?$: $(Y$ or $N).$ If so then this function is almost continuous and could be made continuous by redefining one value of the function namely $f(3\mathrm{.}53).$

To be safe, keep your $x$ values limited to $10$ decimal places.

$\backslash$table$[[x,,f(x)$