Draw the graph of the signum function `f(x)={{:(|x|/x, " when ", x ne0),(0," when ", x=0):}`

Draw the graph of the function " "y=f(x)={:{(|x|/x",","when "x ne 0),(0",","when "x = 0):} From the graph examine the continuity of f(x) at x = 0.

Draw the graph of the function f(x)={{:(x^(2)",", " when ", xlt0),(x",", " when " , 0le x le1),(1//x",", " when " , 1 le x lt oo.):}

Draw the graphs of the constant functions : f(x) = 0

Draw the graph of the following signum function : f(x)=1," when "x gt0 =0," when "x=0 =-1," when "x lt0 Find the domain and range of f(x) from the graph.

Show that the function f(x)={{:(x/|x|",", " when ", x ne0),(1",", " when ", x =0):} is discontinuous at x=0

Draw the graph of the function, f(x)=sqrt(x)(xge0) .

Sketch the graph of the function : " "y=f(x)={:{(-x",", "when "x le 0),(x",", "when "x gt0):} From the graph examine the continuity of f(x) at x = 0.

Draw the graph of the signum function, f:RtoR , defined by f(x)={{:((x)/(|x|)",when "xne0),(0",when "x=0):}orf(x)={{:(1",if "xgt0),(0",if "x=0),(-1",if "xlt0):}

Prove that the function f(x) = {{:(x cos 1/x"," , "when " x != 0),(0",", "when " x = 0):} is continuous at x = 0

Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(x),"when " xne0),(0,"when " x=0):}