Pre-Calculus, 9th edition
29

 PAGE: 88 SET: Exercises PROBLEM: 29

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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