(a)
The functions are and .
Find the domain of .
Since it is a rational function, the denominator should not be the zero.
Thus, the domain of the function is all real numbers except 0 and 2.
The function is .
Since it is a linear function, the domain is all real numbers.
(b)
The function is .
Simplify the function.
Since the above function is a linear function, there is no vertical asymptote.
(c)
The functions are and .
Make the table :
x |
|
|
|
|
|
0 |
|
0 |
1 |
|
1 |
1.5 |
|
1.5 |
2 |
|
2 |
2.5 |
|
2.5 |
3 |
|
3 |
(d)
Graph :
Draw a coordinate plane.
Graph the functions and in the same viewing window.
Graph of the functions and is :
(e)
Observe the above graph.
On a graphing utility, the graphs of f and g will look like the same.
Since there is a finite number of pixels that can be displayed.
There is no discontinuity of f at and .
(a)
The domain of the function is all real numbers except 0 and 2.
The domain of is all real numbers.
(b)
None.
(c)
Completed table is :
x |
|
|
|
|
|
0 |
|
0 |
1 |
|
1 |
1.5 |
|
1.5 |
2 |
|
2 |
2.5 |
|
2.5 |
3 |
|
3 |
(d)
Graph :
(e)
On a graphing utility, the graphs of f and g will look like the same.
Since there is a finite number of pixels that can be displayed.
There is no discontinuity of f at and .
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