To find: all horizontal and vertical asymptotes of the function.
Vertical asymptote:
Horizontal asymptote:
Given information:
The function
Calculation:
Graph of
Let
Putting the value of
And
And
And
Plot the graph:
By inspection of the graph, a vertical asymptote is at
Algebraically, the vertical asymptote corresponds to the fact that
excluded from the domain, as that would cause a division by zero.
Even though
To demonstrate the horizontal asymptote. Right now, it's sufficient to say that, as
approaches infinity, the denominator becomes increasingly larger than the numerator, and the quotient of the division approaches zero.
Therefore, horizontal asymptote:
Chapter 1 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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