a.
To draw: The graph of the given function.
Given:
Calculation:
The given function passes through the points
Since it is an odd function, therefore the graph is symmetric with respect to the origin.
Since the value of the denominator is 0 when
Since the degree of numerator (0) is less than the degree of denominator (1), therefore the horizontal asymptote is
Now the graph is,
b.
To compare: The graph of the given function and
The graph of
Given:
Calculation:
The graph of
Hence, the graph of
c.
To find: The horizontal asymptotes of the graph of
The horizontal asymptote is
Given:
Calculation:
Here, the degree of numerator is 0 and the degree of denominator is 1.
Since the degree of numerator is less than the degree of denominator, therefore the horizontal asymptote is
d.
To find: The vertical asymptotes of the graph of
The vertical asymptote is
The vertical asymptotes must be excluded from the domain of
Given:
Calculation:
The value of the denominator is 0 when
Therefore, the vertical asymptote is
Since the value of the denominator is zero at the vertical asymptotes, therefore the value of the function is undefined at the vertical asymptotes.
Hence, the vertical asymptotes must be excluded from the domain of
Chapter 14 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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