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12 Questions for Questions 9-12 all these steps have to be completed:
a. the domain.
b. the y-intercept.
c. anyx-interceptsthatwecanfindeasily(manytimesthisisnotpossiblewithoutmoreadvanced algebraic methods). Potentially a sign analysis for the function itself that shows where it is above and below the x-axis, but this requires complete knowledge of all x-intercepts.
d. any even or odd symmetry.
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4.7 Curve Sketch Analysis of Rational Functions 311
e. the behavior of the function at any non-domain points, meaning the limits as x → c for any value x ＝ c not in the domain of the function. We make special note of any holes or vertical asymptotes.
f. the ″end behavior″ of the graph, meaning the limits as x → ±∞. We make special note of any horizontal asymptotes.
g. any local minima or maxima, along with where the function is increasing and decreasing using the first derivative.
h. any inflection points and where the function is concave up and concave down using the second derivative.
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