Question

Let f (x) = {√-x ,if x <0

{3-x ,if 0《x <3

{(x-3)^2 ,if x>3

(A) Check whether for is discontinuous.if yes l,find where?

(B) Give a rough sketch of the graph of f.

Answer 1

$y=\left\{ \begin{matrix} \sqrt{-x} , x<0 \\ 3-x, 0\leq x<3\\ (x-3)^2, x>3 \end{matrix}\right.$

$x=0\\ \lim\limits_{x\to0-0}\sqrt{-x}=0\\ \lim\limits_{x\to0+0}(3-x)=3\\$

 The function at the point $x=0$ has a jump discontinuity

$x=3\\ \lim\limits_{x\to3-0}(3-x)=0\\ \lim\limits_{x\to3+0}(x-3)^2=0\\$

The function  is a continuous at the point $x=3$ .

The function  is discontinuous at $x=0$.