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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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