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Graph the piecewise-defined function.

Graph the piecewise-defined function.-example-1
Graph the piecewise-defined function.-example-1
Graph the piecewise-defined function.-example-2
Graph the piecewise-defined function.-example-3
Graph the piecewise-defined function.-example-4
Graph the piecewise-defined function.-example-5
User Nim J
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Answer:

We are asked to graph the function:

f(x)= sin x ; if x≤ 0

and |x| ; if x > 0

We know that the function |x| is evaluated as:

|x|= -x ; if x≤0

and x ; if x > 0

Hence, we have to graph the function:

f(x) = sin x ; if x ≤ 0

and x ; if x > 0

Also the function is continuous at x=0.

Since the Left hand limit and the right hand limit of the function exist and is equal to the value of the function at x=0.

i.e. f(0)=0.

The graph is plotted as the graph of sin (x) in the region (-∞,0] and y=x in the region (0,∞).

Graph the piecewise-defined function.-example-1
User Shmiddty
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