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.`

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 follwos : f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):} Examine whether underset(xrarr1)"lim"f(x) exists 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.

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

A continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

A function F(x) is defined as follows: F(x)={:{(1+2x,"when "xle1),(3-2x,"when "x gt1):} Determine F(0), F(-1.5),F(1), F(2.6) and F(x+2).

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that 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 f (x) is defined as follows: f(x)={{:(x^(4)-3,"when " xle2),(x^(3)+5,"when "xgt2):} Prove that the function f (x) is continuous at x = 2 .