A function f(x) is defined as follows :
`f(x)=x," when "x gt0`
`=-x," when "x lt0`
`=-1," when "x=0`
Sketch the graph of f(x) and from the graph examine its continuity at x = 0.

A function f(x) is defined as follows : f(x)=-x," when "x lt0 =2," when "0 lex lt2 =4-x," when "x ge2 Draw the graph of the function and from the graph examine whether f(x) is continuous at x = 0 and x = 2 or not.

A function f(x) is defined as follows : f(x)=x," when "x lt1 =x+1," when "x gt1 =3/2," when "x=1 Draw the graph of f(x) and examine its continuity at x=(1)/(2)and x=1.

Sketch the graph of f(x)=(|x|)/(x), f(0)=1. From the graph examine the continuity of f(x) at x = 0.

Sketch the graph of the function f(x)=(4)/(x). From the graph examine the continuity of f(x) at x = 0.

Given, f (x) = x when x ge 0 = - x , when x lt 0

Sketch the graph of f(x)=|x-4|-2. From the graph examine whether f(x) is continuous at x = 4 or not.

A function f(x) is defined as follows : " "f(x)={:{(x-1",","when "x gt 0),(-(1)/(2)",","when "x = 0),( x+1",","when "xlt0):} Draw the graph of the function f(x). From the graph find the value of f(x) at x=-(1)/(2) and examine whether f(x) is continuous at x = 0.

A function f(x) is defined as follows: f(x)={:{(1",","when x is an integer"),(0",","when x is not an integer"):} Draw the graph of the function and from the graph find its points of discontinuity (if any).

A function phi(x) is defined as follows : phi(x)=2," when x is an integer" =0," when x is not an integer" Draw the graphs of the function and from the graph find the points of discontinuity of phi(x).

A function f (x) is defined as follows : f (x)={{:(x,"when "xge0),(-x,"when " x lt0):} Examine the cotinuity and differentiability of (x) at x= 0 .