To draw: graph to illustrate the given asymptote.
Answer to Problem 2CFU
The vertical and horizontal asymptote in the above graph is
The vertical and horizontal asymptote in the above graph is
The vertical and slant asymptote in the above graph is
Explanation of Solution
Given information:
Types of asymptotes to be illustrated are as follows:
Vertical
Horizontal
Slant
Calculation:
The types of asymptotes are discussed below.
Case 1:
The graph for
In this case, vertical asymptote is value of
Since the denominator of the function is of higher degree than the numerator, then the horizontal asymptote will be x-axis. Horizontal asymptote is
Case 2:
The graph for
Since the numerator and denominator of the function are of same degree, then the horizontal asymptote will fraction of leading coefficient. For this case, it is
It is clear shown in the graph that the vertical asymptotes for this case is
Case 3:
The graph for
It is clear shown in the graph that the vertical asymptotes for this case is
Since the numerator is exactly one degree higher than that of the denominator, then slant asymptote is present. Divide the numerator by the denominator to get the quotient as slant asymptote.
Thus, the slant asymptote is
Chapter 3 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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