The piecewise function is

**( a)**

All possible values of * *for which the function is mathematically correct is the domain of a function.

The domain of is all real numbers.

**( b)**

Find the intercepts

Find the -intercept by substituting .

If , the function is .

Substitute in above function.

The value of which is not to be considered because .

There is no -intercept.

Find the -intercept by substituting .

The function is not defined at .

The function is defined at .

The intercept is .

**( c)**

Draw the table of different values of for .

If then the function is .

If then the function is .

** Graph:**

1). Draw a coordinate plane.

2). Plot the points found in the table and connect the plotted points

3). Label the intercept points.

** ( d)**

All possible values of * *is range of a function.

Observe the graph:

The range of function is .

The range in interval notation .

**( e)**

The function is discontinuous at because the function has hole as .

**( a)** The domain of is all real numbers.

**( b)** The intercept is .

**( c)** Graph of the function:

**( d)** The range of the function in interval notation .

**( e)** The function is discontinuous at .

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