$[20]7.$ Let

$x-3,x^2-4x4$

$1,f(x)=\{\begin{array}{ccc}\sqrt[\phantom{2}]{-x}& if& x<mn>0</mn>\\ 3-x& if& 0x<mn>2</mn>\\ (x-2{)}^2& if& x>2\end{array}$

$x,x-3,x^2-4x4$

$(5-2)(2)$

$2($a$)$ Sketch the graph of $f(x)$ with values on $x-y$ axes appropriately. State the intervals on which $f$ is continuous. $f(x)$ a continoous at $3$ from the left $(-,0)$

$3($b$)$ State the numbers at which continizan at of frem the theontinuous with reason and types or discontinuity.

$0,2$

$f(x)$ is Discantinuey at O$,$ because the graph jumps from one Point to the other.

$4($c$)$ Evaluate each limit$,$ if it exists.

$($i$)\underset{x0}{lim}f(x)=3$

$($ii$)\underset{x}{lim}f(x)=$

$($iii$)\underset{x0-}{lim}f(x)=$

$($iv$)\underset{x3}{lim}f(x)=$