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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
.
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If then the function is
.
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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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