The asymptotes and intercepts, describe the behaviour of vertical asymptotes using limits, analyse and graph the function.
The vertical asymptote is
Given:
The function is
Concept Used:
If a polynomial function in the form
And,
The end behaviour asymptote given by
The condition can be concluded as,
1) If
2) If
3) If
And,
The x -intercept is given by zeros of numerator that are not zero of denominator. And y -intercept is given by
From using asymptotes and intercepts the graph can be drawn.
Calculation:
Consider the function,
To find vertical asymptotes, find the zeros of denominator, so factorize the denominator
Thus, the zeros of denominator of
To find the behaviour of vertical asymptotes, compute the limit when x approaches to
To find end behaviour asymptotes, find
Since,
Now find the intercept, the x -intercept is given by zeros of numerator that are not zero of denominator.
Hence, solve
And y -intercept is given by
Thus y -intercept is
Hence, using vertical asymptotes,
Interpretations form graph:
1) Domain of
2) Range is
3) Continuous everywhere except
4) Decreasing in
5) No extremes.
6) Not symmetric.
7) Unbounded.
Conclusion:
The vertical asymptote is
Chapter 2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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